(NOT-<-OF-+-1-OF-MAXELEM
 (38890 54 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (10896 221 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (10372 221 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (10256 217 (:REWRITE ALL-<-TRANSITIVE))
 (7150 276 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (7065 7065 (:TYPE-PRESCRIPTION NAT-LISTP))
 (6733 1826 (:REWRITE DEFAULT-+-2))
 (6214 3107 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-2))
 (6149 3107 (:TYPE-PRESCRIPTION RATIONALP-OF-MAXELEM))
 (6082 3041 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (5228 697 (:REWRITE DEFAULT-<-1))
 (4630 2315 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (4395 104 (:REWRITE USE-ALL-<-FOR-CAR))
 (3487 3487 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (2959 89 (:REWRITE RATIONALP-OF-MAXELEM))
 (2595 697 (:REWRITE DEFAULT-<-2))
 (2514 89 (:DEFINITION RATIONAL-LISTP))
 (2437 245 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (2316 2316 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (2315 2315 (:TYPE-PRESCRIPTION DARGP))
 (2315 2315 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (2315 2315 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (2315 2315 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (1826 1826 (:REWRITE DEFAULT-+-1))
 (1337 184 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (1266 633 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (1134 54 (:REWRITE <=-OF-MAXELEM-WHEN-MEMBER-EQUAL))
 (1068 340 (:REWRITE +-COMBINE-CONSTANTS))
 (1052 183 (:REWRITE ALL-RATIONALP-OF-CDR))
 (914 751 (:REWRITE DEFAULT-CDR))
 (872 340 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (864 54 (:DEFINITION MEMBER-EQUAL))
 (855 67 (:REWRITE ALL-<-OF-+-OF-1-AND-MAXELEM))
 (819 697 (:REWRITE USE-ALL-<))
 (808 808 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (797 404 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (697 697 (:REWRITE USE-ALL-<-2))
 (688 688 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (677 54 (:REWRITE USE-ALL-<=-FOR-CAR))
 (673 673 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (635 503 (:REWRITE DEFAULT-CAR))
 (468 78 (:REWRITE NAT-LISTP-OF-CDR))
 (404 404 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (388 340 (:DEFINITION FIX))
 (378 126 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (378 126 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (356 178 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (340 38 (:REWRITE ALL-<=-OF-CDR))
 (335 335 (:REWRITE USE-ALL-RATIONALP-2))
 (335 335 (:REWRITE USE-ALL-RATIONALP))
 (330 330 (:TYPE-PRESCRIPTION ALL-NATP))
 (329 329 (:REWRITE MAXELEM-WHEN-NON-CONSP))
 (297 119 (:REWRITE ACL2-NUMBERP-OF-MAXELEM))
 (284 142 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (270 270 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (217 92 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (216 216 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (208 104 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (194 194 (:REWRITE USE-ALL-<=-2))
 (194 194 (:REWRITE USE-ALL-<=))
 (184 184 (:TYPE-PRESCRIPTION ALL-<=))
 (178 178 (:TYPE-PRESCRIPTION INTEGER-LISTP))
 (177 128 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (142 142 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (128 128 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (128 128 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (122 122 (:TYPE-PRESCRIPTION MEMBERP))
 (112 112 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (112 112 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (108 108 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (108 108 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (92 92 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (92 92 (:REWRITE ALL-<=-MONOTONE))
 (89 89 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (20 10 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (14 14 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (14 14 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (10 10 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (10 10 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 )
(ENSURE-SUBSTITUTABLE-VAR
 (248 124 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (247 247 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (245 19 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (124 124 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (56 15 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (50 16 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (40 1 (:DEFINITION MEMBER-EQUAL))
 (36 18 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS-WHEN-ARRAY1P))
 (33 33 (:TYPE-PRESCRIPTION LEN))
 (32 5 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (32 5 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (31 31 (:TYPE-PRESCRIPTION NAT-LISTP))
 (30 25 (:REWRITE DEFAULT-<-2))
 (30 4 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-2))
 (25 25 (:REWRITE USE-ALL-<-2))
 (25 25 (:REWRITE USE-ALL-<))
 (25 25 (:REWRITE DEFAULT-<-1))
 (25 9 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (22 9 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (19 19 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (19 19 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (18 9 (:TYPE-PRESCRIPTION POSP-OF-CAR-OF-DIMENSIONS-WHEN-ARRAY1P))
 (18 5 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (16 16 (:REWRITE USE-ALL-<=-2))
 (16 16 (:REWRITE USE-ALL-<=))
 (15 5 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (15 5 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (10 5 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (10 5 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (10 5 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (9 9 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (9 9 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (8 8 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (8 4 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (7 7 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (6 6 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (5 5 (:TYPE-PRESCRIPTION MYQUOTEP))
 (5 5 (:TYPE-PRESCRIPTION DARGP))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (5 5 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (5 5 (:REWRITE DARGP-LESS-THAN-MONO))
 (4 4 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (4 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (3 3 (:REWRITE USE-ALL-NATP-2))
 (3 3 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (2 2 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(FIND-VAR-AND-EXPR-TO-SUBST
 (13 13 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 )
(NATP-OF-MV-NTH-2-OF-FIND-VAR-AND-EXPR-TO-SUBST
 (1519 76 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (1342 671 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (686 343 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (671 671 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (439 439 (:TYPE-PRESCRIPTION NAT-LISTP))
 (280 35 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-NOT-CONSP))
 (275 11 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (253 11 (:LINEAR LEN-OF-CDR-LINEAR))
 (240 35 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-2))
 (236 96 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (204 182 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (182 182 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (182 182 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (182 182 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (180 13 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (166 48 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (166 48 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (140 35 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (138 101 (:REWRITE DEFAULT-<-2))
 (127 92 (:REWRITE DEFAULT-+-2))
 (110 55 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (101 101 (:REWRITE USE-ALL-<-2))
 (101 101 (:REWRITE USE-ALL-<))
 (101 101 (:REWRITE DEFAULT-<-1))
 (89 89 (:REWRITE DEFAULT-+-1))
 (83 83 (:REWRITE DEFAULT-CDR))
 (76 76 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (76 76 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (70 70 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (69 23 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (55 55 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (44 44 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (39 39 (:REWRITE USE-ALL-<=-2))
 (39 39 (:REWRITE USE-ALL-<=))
 (39 39 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (35 35 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (35 35 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (35 35 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (35 35 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (35 35 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (35 35 (:REWRITE DEFAULT-CAR))
 (33 11 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (32 32 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (26 13 (:REWRITE DARGP-WHEN-NATP-CHEAP))
 (26 13 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (23 23 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (16 16 (:REWRITE USE-ALL-NATP-2))
 (16 16 (:REWRITE USE-ALL-NATP))
 (13 13 (:TYPE-PRESCRIPTION MYQUOTEP))
 (13 13 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (11 11 (:REWRITE USE-ALL-RATIONALP-2))
 (11 11 (:REWRITE USE-ALL-RATIONALP))
 (6 3 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (4 4 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (3 3 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (3 3 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (2 2 (:REWRITE EQUAL-OF-LEN-AND-0))
 )
(<-OF-MV-NTH-2-OF-FIND-VAR-AND-EXPR-TO-SUBST
 (1290 61 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (956 478 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (591 591 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (478 478 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (386 193 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (280 280 (:TYPE-PRESCRIPTION NAT-LISTP))
 (260 87 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (202 101 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (160 117 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (159 35 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (159 35 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (150 6 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (138 6 (:LINEAR LEN-OF-CDR-LINEAR))
 (136 106 (:REWRITE DEFAULT-<-2))
 (134 106 (:REWRITE DEFAULT-<-1))
 (121 20 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (117 117 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (117 117 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (106 106 (:REWRITE USE-ALL-<-2))
 (106 106 (:REWRITE USE-ALL-<))
 (101 101 (:TYPE-PRESCRIPTION DARGP))
 (88 11 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-NOT-CONSP))
 (64 50 (:REWRITE DEFAULT-+-2))
 (61 61 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (61 61 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (51 17 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (51 17 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (48 48 (:REWRITE USE-ALL-<=-2))
 (48 48 (:REWRITE USE-ALL-<=))
 (48 48 (:REWRITE DEFAULT-+-1))
 (48 12 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (44 44 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (43 43 (:REWRITE DEFAULT-CDR))
 (40 16 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (34 17 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (31 17 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (30 12 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (24 24 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (22 22 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (20 20 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (17 17 (:TYPE-PRESCRIPTION MYQUOTEP))
 (17 17 (:REWRITE DEFAULT-CAR))
 (17 17 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (17 17 (:REWRITE DARGP-LESS-THAN-MONO))
 (13 13 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (12 12 (:REWRITE USE-ALL-RATIONALP-2))
 (12 12 (:REWRITE USE-ALL-RATIONALP))
 (12 12 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (11 11 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (11 11 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (11 11 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (7 7 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (6 6 (:REWRITE USE-ALL-NATP-2))
 (6 6 (:REWRITE USE-ALL-NATP))
 (6 3 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (3 3 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (3 3 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (3 3 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (2 2 (:REWRITE EQUAL-OF-LEN-AND-0))
 )
(DARGP-OF-MV-NTH-3-OF-FIND-VAR-AND-EXPR-TO-SUBST
 (1306 87 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (650 325 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (325 325 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (304 152 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (218 218 (:TYPE-PRESCRIPTION NAT-LISTP))
 (192 24 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-NOT-CONSP))
 (183 24 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-2))
 (168 66 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (124 106 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (117 33 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (117 33 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (106 106 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (106 106 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (106 106 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (104 52 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (103 72 (:REWRITE DEFAULT-<-2))
 (100 4 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (96 24 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (92 4 (:LINEAR LEN-OF-CDR-LINEAR))
 (87 87 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (87 87 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (85 44 (:REWRITE DEFAULT-+-2))
 (78 26 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (75 72 (:REWRITE DEFAULT-<-1))
 (72 72 (:REWRITE USE-ALL-<-2))
 (72 72 (:REWRITE USE-ALL-<))
 (72 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (52 52 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (48 48 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (44 44 (:REWRITE DEFAULT-+-1))
 (42 14 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (38 38 (:REWRITE DEFAULT-CDR))
 (36 36 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (32 16 (:REWRITE DARGP-WHEN-NATP-CHEAP))
 (32 16 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (26 26 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (24 24 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (24 24 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (24 24 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (24 24 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (24 24 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (22 22 (:REWRITE DEFAULT-CAR))
 (16 16 (:TYPE-PRESCRIPTION NATP))
 (16 16 (:TYPE-PRESCRIPTION MYQUOTEP))
 (16 8 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (14 14 (:REWRITE USE-ALL-RATIONALP-2))
 (14 14 (:REWRITE USE-ALL-RATIONALP))
 (12 12 (:REWRITE USE-ALL-<=-2))
 (12 12 (:REWRITE USE-ALL-<=))
 (12 12 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (12 12 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (8 8 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (6 6 (:REWRITE USE-ALL-NATP-2))
 (6 6 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (2 2 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (2 2 (:REWRITE EQUAL-OF-LEN-AND-0))
 )
(DARGP-LESS-THAN-OF-MV-NTH-3-OF-FIND-VAR-AND-EXPR-TO-SUBST
 (937 48 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (500 250 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (419 419 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (294 147 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (250 250 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (216 216 (:TYPE-PRESCRIPTION NAT-LISTP))
 (194 69 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (158 79 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (125 5 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (121 93 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (115 5 (:LINEAR LEN-OF-CDR-LINEAR))
 (107 24 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (107 24 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (93 93 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (93 93 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (93 14 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (87 66 (:REWRITE DEFAULT-<-2))
 (79 79 (:TYPE-PRESCRIPTION DARGP))
 (68 66 (:REWRITE DEFAULT-<-1))
 (66 66 (:REWRITE USE-ALL-<-2))
 (66 66 (:REWRITE USE-ALL-<))
 (63 21 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (56 7 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-NOT-CONSP))
 (48 48 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (48 48 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (46 38 (:REWRITE DEFAULT-+-2))
 (42 21 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (38 38 (:REWRITE DEFAULT-CDR))
 (38 38 (:REWRITE DEFAULT-+-1))
 (34 18 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (32 8 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (30 30 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (23 23 (:REWRITE USE-ALL-<=-2))
 (23 23 (:REWRITE USE-ALL-<=))
 (22 8 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (21 21 (:TYPE-PRESCRIPTION MYQUOTEP))
 (18 18 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (16 16 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (14 14 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (14 14 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (14 14 (:REWRITE DEFAULT-CAR))
 (9 9 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (8 8 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (8 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (7 7 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (7 7 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (7 7 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 3 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (5 5 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (3 3 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (3 3 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (2 2 (:REWRITE USE-ALL-RATIONALP-2))
 (2 2 (:REWRITE USE-ALL-RATIONALP))
 (2 2 (:REWRITE EQUAL-OF-LEN-AND-0))
 )
(CHECK-FOR-VAR-SUBST-LITERAL
 (1011 368 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (768 37 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (726 594 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (630 249 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (340 340 (:TYPE-PRESCRIPTION NAT-LISTP))
 (334 180 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (252 2 (:REWRITE DARGP-LESS-THAN-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (240 240 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (198 99 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (197 99 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (180 180 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (173 27 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (173 27 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (165 45 (:REWRITE DEFAULT-+-2))
 (148 74 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (128 65 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (120 5 (:REWRITE ACL2-NUMBERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (99 99 (:TYPE-PRESCRIPTION DARGP))
 (99 99 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (99 99 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (99 99 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (97 97 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (75 65 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (66 48 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS-WHEN-ARRAY1P))
 (65 65 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (62 35 (:REWRITE DEFAULT-<-2))
 (60 30 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (60 10 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (45 45 (:REWRITE DEFAULT-+-1))
 (37 37 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (37 37 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (37 35 (:REWRITE DEFAULT-<-1))
 (35 35 (:REWRITE USE-ALL-<-2))
 (35 35 (:REWRITE USE-ALL-<))
 (33 24 (:TYPE-PRESCRIPTION POSP-OF-CAR-OF-DIMENSIONS-WHEN-ARRAY1P))
 (28 28 (:REWRITE DEFAULT-CAR))
 (20 10 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (20 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (18 18 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (16 16 (:REWRITE USE-ALL-<=-2))
 (16 16 (:REWRITE USE-ALL-<=))
 (16 5 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (14 7 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (11 11 (:TYPE-PRESCRIPTION ALL-NATP))
 (11 2 (:REWRITE NOT-<-OF-NTH-OF-DARGS-OF-AREF1-AND-CONSTANT-WHEN-PSEUDO-DAG-ARRAYP))
 (10 10 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (8 2 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (7 7 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (7 7 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (4 4 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 1 (:REWRITE <-OF-NTH-OF-0-AND-0-WHEN-ALL-NATP-CHEAP))
 (1 1 (:REWRITE NOT-<-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-2))
 )
(NATP-OF-MV-NTH-2-OF-CHECK-FOR-VAR-SUBST-LITERAL
 (86 43 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (72 36 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (70 35 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (70 29 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (66 28 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (59 59 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (58 58 (:TYPE-PRESCRIPTION NAT-LISTP))
 (58 29 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (58 2 (:REWRITE DEFAULT-CDR))
 (56 56 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (52 26 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (44 22 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (44 4 (:REWRITE <-OF-0-AND-LEN))
 (41 21 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (38 21 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (38 11 (:REWRITE DEFAULT-+-2))
 (36 36 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (36 36 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (29 29 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (29 29 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (29 29 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (27 27 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (24 1 (:REWRITE ACL2-NUMBERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (21 21 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (18 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (14 4 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (13 13 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (11 11 (:REWRITE DEFAULT-+-1))
 (11 4 (:REWRITE DEFAULT-<-2))
 (9 9 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (8 1 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (8 1 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (2 2 (:TYPE-PRESCRIPTION ALL-NATP))
 (2 2 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (2 1 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (1 1 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(<-MV-NTH-2-OF-CHECK-FOR-VAR-SUBST-LITERAL
 (133 2 (:REWRITE DARGP-LESS-THAN-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (90 45 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (90 35 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (74 37 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (74 33 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (72 36 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (67 67 (:TYPE-PRESCRIPTION NAT-LISTP))
 (66 33 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (61 61 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (58 2 (:REWRITE DEFAULT-CDR))
 (56 56 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (56 30 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (52 26 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (50 30 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (44 22 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (44 4 (:REWRITE <-OF-0-AND-LEN))
 (43 16 (:REWRITE DEFAULT-+-2))
 (38 38 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (36 36 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (36 36 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (34 1 (:REWRITE NATP-OF-+-WHEN-NATP-AND-NATP))
 (33 33 (:TYPE-PRESCRIPTION DARGP))
 (33 33 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (33 33 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (33 33 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (30 30 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (24 1 (:REWRITE ACL2-NUMBERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (20 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (18 3 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (18 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (16 16 (:REWRITE DEFAULT-+-1))
 (13 13 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (11 4 (:REWRITE DEFAULT-<-2))
 (9 9 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (8 1 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (8 1 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (6 3 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (5 5 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION ALL-NATP))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (3 3 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 1 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (1 1 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(DARGP-LESS-THAN-OF-MV-NTH-3-OF-CHECK-FOR-VAR-SUBST-LITERAL
 (133 2 (:REWRITE DARGP-LESS-THAN-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (90 45 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (90 35 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (74 37 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (74 33 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (72 36 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (67 67 (:TYPE-PRESCRIPTION NAT-LISTP))
 (66 33 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (61 61 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (58 2 (:REWRITE DEFAULT-CDR))
 (56 56 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (56 30 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (52 26 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (50 30 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (44 22 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (44 4 (:REWRITE <-OF-0-AND-LEN))
 (43 16 (:REWRITE DEFAULT-+-2))
 (38 38 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (36 36 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (36 36 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (34 1 (:REWRITE NATP-OF-+-WHEN-NATP-AND-NATP))
 (33 33 (:TYPE-PRESCRIPTION DARGP))
 (33 33 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (33 33 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (33 33 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (30 30 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (24 1 (:REWRITE ACL2-NUMBERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (20 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (18 3 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (18 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (16 16 (:REWRITE DEFAULT-+-1))
 (13 13 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (11 4 (:REWRITE DEFAULT-<-2))
 (9 9 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (8 1 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (8 1 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (6 3 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (5 5 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION ALL-NATP))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (3 3 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 1 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (1 1 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(DARGP-LESS-THAN-OF-MV-NTH-3-OF-CHECK-FOR-VAR-SUBST-LITERAL-GEN
 (60 60 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (7 4 (:REWRITE DEFAULT-<-1))
 (6 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (6 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (4 4 (:TYPE-PRESCRIPTION NAT-LISTP))
 (4 4 (:REWRITE USE-ALL-<=-2))
 (4 4 (:REWRITE USE-ALL-<=))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 2 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (4 2 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (3 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 1 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:REWRITE USE-ALL-RATIONALP-2))
 (1 1 (:REWRITE USE-ALL-RATIONALP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 )
(DARGP-OF-MV-NTH-3-OF-CHECK-FOR-VAR-SUBST-LITERAL
 (57 57 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 1 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (3 1 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (2 2 (:TYPE-PRESCRIPTION NAT-LISTP))
 (2 1 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (2 1 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (2 1 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (2 1 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-MONO))
 )
(NATP-OF-MV-NTH-3-OF-CHECK-FOR-VAR-SUBST-LITERAL
 (57 57 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (28 4 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (10 2 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE USE-ALL-<-2))
 (6 6 (:REWRITE USE-ALL-<))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (4 4 (:TYPE-PRESCRIPTION LEN))
 (4 4 (:REWRITE USE-ALL-<=-2))
 (4 4 (:REWRITE USE-ALL-<=))
 (4 4 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (4 4 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (3 1 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (3 1 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (2 2 (:TYPE-PRESCRIPTION NAT-LISTP))
 (2 2 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (2 1 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (2 1 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (2 1 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (2 1 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-MONO))
 )
(SUBSTITUTE-A-VAR
 (174 7 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (120 120 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS-WHEN-ARRAY1P))
 (60 60 (:TYPE-PRESCRIPTION POSP-OF-CAR-OF-DIMENSIONS-WHEN-ARRAY1P))
 (29 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (21 7 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (21 7 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (18 9 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (16 9 (:REWRITE DEFAULT-<-2))
 (15 11 (:REWRITE USE-ALL-<))
 (11 11 (:REWRITE USE-ALL-<-2))
 (9 9 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (9 9 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (9 9 (:REWRITE DEFAULT-<-1))
 (9 2 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (7 7 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (7 7 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (6 5 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (6 3 (:REWRITE REMOVE-EQUAL-WHEN-NOT-MEMBER-EQUAL-CHEAP))
 (6 3 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (5 5 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (5 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (5 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (4 4 (:TYPE-PRESCRIPTION MEMBERP))
 (4 4 (:REWRITE USE-ALL-<=-2))
 (4 4 (:REWRITE USE-ALL-<=))
 (4 4 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (4 4 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (4 4 (:REWRITE ALL-<-TRANSITIVE))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION MYQUOTEP))
 (3 3 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (3 3 (:TYPE-PRESCRIPTION ALL-NATP))
 (3 3 (:REWRITE REMOVE-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (3 2 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DARGP-LESS-THAN-MONO))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (1 1 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (1 1 (:REWRITE NOT-<-OF-NTH-WHEN-BOUNDED-DARG-LISTP-GEN-CONSTANT))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (1 1 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 )
(LEN-OF-MV-NTH-3-OF-SUBSTITUTE-A-VAR
 (1392 14 (:REWRITE LEN-OF-REMOVE-EQUAL-WHEN-NO-DUPLICATESP-EQUAL))
 (1350 14 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (1238 43 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (264 132 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (252 14 (:REWRITE LEN-OF-CDR))
 (246 14 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (232 106 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (169 53 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (169 53 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (162 162 (:TYPE-PRESCRIPTION NAT-LISTP))
 (146 132 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (132 132 (:TYPE-PRESCRIPTION DARGP))
 (132 132 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (132 132 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (132 132 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (112 56 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (105 53 (:REWRITE DEFAULT-<-2))
 (96 96 (:REWRITE DEFAULT-CAR))
 (64 32 (:REWRITE REMOVE-EQUAL-WHEN-NOT-MEMBER-EQUAL-CHEAP))
 (63 53 (:REWRITE DEFAULT-<-1))
 (53 53 (:REWRITE USE-ALL-<-2))
 (53 53 (:REWRITE USE-ALL-<))
 (47 47 (:REWRITE DEFAULT-CDR))
 (43 43 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (43 43 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (32 32 (:REWRITE REMOVE-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (32 32 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (28 14 (:REWRITE DEFAULT-+-2))
 (20 20 (:TYPE-PRESCRIPTION REMOVE-EQUAL))
 (20 10 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (18 9 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (14 14 (:REWRITE EQUAL-OF-LEN-AND-0))
 (14 14 (:REWRITE DEFAULT-+-1))
 (14 14 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (10 10 (:REWRITE USE-ALL-<=-2))
 (10 10 (:REWRITE USE-ALL-<=))
 (9 9 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (9 9 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (9 9 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 )
(NATP-OF-MV-NTH-5-OF-SUBSTITUTE-A-VAR
 (3990 1907 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (2692 434 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (2524 724 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (2522 785 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (2341 2341 (:TYPE-PRESCRIPTION NAT-LISTP))
 (1570 785 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (1515 255 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (1371 1371 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (1196 504 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (1008 504 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (893 893 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (858 272 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (785 785 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (724 724 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (724 724 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (658 14 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-ALT))
 (657 148 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (536 70 (:REWRITE DEFAULT-+-2))
 (460 64 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (439 19 (:REWRITE DEFAULT-CDR))
 (398 255 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (364 14 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (322 28 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-BOUNDED-DAG-EXPRP-OF-AREF1))
 (322 23 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (296 148 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (272 272 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (255 255 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (246 15 (:REWRITE CONSP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE-IFF))
 (220 220 (:REWRITE DEFAULT-CAR))
 (210 28 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (204 104 (:REWRITE DEFAULT-<-2))
 (192 42 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (148 148 (:TYPE-PRESCRIPTION DARGP))
 (148 148 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (148 148 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (148 148 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (126 14 (:REWRITE INTEGERP-OF-NTH-WHEN-ALL-INTEGERP))
 (120 20 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-OF-CAR))
 (115 23 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (112 14 (:REWRITE INTEGERP-OF-NTH-OF-DARGS))
 (108 6 (:REWRITE EQUAL-OF-LEN-AND-0))
 (104 104 (:REWRITE USE-ALL-<-2))
 (104 104 (:REWRITE USE-ALL-<))
 (104 104 (:REWRITE DEFAULT-<-1))
 (104 26 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (102 102 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (98 28 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (84 14 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (70 70 (:REWRITE DEFAULT-+-1))
 (60 60 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (58 58 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (56 56 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (56 14 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (52 52 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (51 51 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (50 25 (:REWRITE REMOVE-EQUAL-WHEN-NOT-MEMBER-EQUAL-CHEAP))
 (47 47 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (46 46 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (46 46 (:REWRITE USE-ALL-<=-2))
 (46 46 (:REWRITE USE-ALL-<=))
 (40 40 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (34 34 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (28 28 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (28 28 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (28 28 (:REWRITE DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (28 28 (:REWRITE DAG-EXPRP-WHEN-BOUNDED-DAG-EXPRP))
 (28 14 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (28 14 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (26 26 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (26 26 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (25 25 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (25 25 (:REWRITE REMOVE-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (23 23 (:REWRITE USE-ALL-RATIONALP-2))
 (23 23 (:REWRITE USE-ALL-RATIONALP))
 (23 23 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (23 23 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (20 20 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (20 20 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (20 20 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (14 14 (:TYPE-PRESCRIPTION MYQUOTEP))
 (14 14 (:TYPE-PRESCRIPTION ALL-NATP))
 (14 14 (:REWRITE INTEGERP-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (14 14 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (14 14 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (14 14 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (14 14 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (14 14 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-BETTER))
 (14 14 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-GEN))
 (14 14 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (14 14 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (13 13 (:REWRITE USE-ALL-NATP-2))
 (13 13 (:REWRITE USE-ALL-NATP))
 (9 3 (:REWRITE TYPE-OF-REBUILD-LITERALS-WITH-SUBSTITUTION-TWO))
 (6 6 (:TYPE-PRESCRIPTION WF-DAGP))
 (6 6 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(BOUND-ON-MV-NTH-5-OF-SUBSTITUTE-A-VAR-3
 (2598 1229 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (1806 296 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (1726 476 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (1720 558 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (1525 1525 (:TYPE-PRESCRIPTION NAT-LISTP))
 (1116 558 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (920 920 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (887 167 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (742 304 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (648 648 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (608 304 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (569 120 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (558 558 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (517 11 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-ALT))
 (516 163 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (476 476 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (476 476 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (467 61 (:REWRITE DEFAULT-+-2))
 (439 19 (:REWRITE DEFAULT-CDR))
 (376 51 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (295 25 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (286 11 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (260 167 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (253 22 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-BOUNDED-DAG-EXPRP-OF-AREF1))
 (246 15 (:REWRITE CONSP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE-IFF))
 (240 120 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (184 184 (:TYPE-PRESCRIPTION NATP))
 (181 94 (:REWRITE DEFAULT-<-2))
 (167 167 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (165 22 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (163 163 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (147 147 (:REWRITE DEFAULT-CAR))
 (124 94 (:REWRITE DEFAULT-<-1))
 (120 120 (:TYPE-PRESCRIPTION DARGP))
 (120 120 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (120 120 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (120 120 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (114 30 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (108 6 (:REWRITE EQUAL-OF-LEN-AND-0))
 (100 20 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (94 94 (:REWRITE USE-ALL-<-2))
 (94 94 (:REWRITE USE-ALL-<))
 (89 89 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (88 11 (:REWRITE INTEGERP-OF-NTH-OF-DARGS))
 (87 11 (:REWRITE INTEGERP-OF-NTH-WHEN-ALL-INTEGERP))
 (84 14 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-OF-CAR))
 (77 22 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (68 17 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (66 11 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (61 61 (:REWRITE DEFAULT-+-1))
 (48 48 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (48 48 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (46 46 (:REWRITE USE-ALL-<=-2))
 (46 46 (:REWRITE USE-ALL-<=))
 (44 44 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (42 42 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (40 40 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (34 34 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (34 17 (:REWRITE REMOVE-EQUAL-WHEN-NOT-MEMBER-EQUAL-CHEAP))
 (32 11 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (28 28 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (27 27 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (25 25 (:REWRITE USE-ALL-RATIONALP-2))
 (25 25 (:REWRITE USE-ALL-RATIONALP))
 (22 22 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (22 22 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (22 22 (:REWRITE DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (22 22 (:REWRITE DAG-EXPRP-WHEN-BOUNDED-DAG-EXPRP))
 (22 11 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (22 11 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (20 20 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (20 20 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (17 17 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (17 17 (:REWRITE REMOVE-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (17 17 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (17 17 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (16 16 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (14 14 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (14 14 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (14 14 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (11 11 (:TYPE-PRESCRIPTION MYQUOTEP))
 (11 11 (:TYPE-PRESCRIPTION ALL-NATP))
 (11 11 (:REWRITE INTEGERP-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (11 11 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (11 11 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (11 11 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (11 11 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (11 11 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-BETTER))
 (11 11 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-GEN))
 (11 11 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (11 11 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (9 3 (:REWRITE TYPE-OF-REBUILD-LITERALS-WITH-SUBSTITUTION-TWO))
 (6 6 (:TYPE-PRESCRIPTION WF-DAGP))
 (6 6 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(BOUND-ON-MV-NTH-5-OF-SUBSTITUTE-A-VAR-3-GEN)
(TYPE-OF-SUBSTITUTE-A-VAR
 (4063 1020 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (2322 1161 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (1754 469 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (1427 198 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (1287 505 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (1200 60 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (1190 62 (:REWRITE DEFAULT-CDR))
 (1188 1161 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (1072 536 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (1068 1068 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (938 469 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (911 526 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (800 355 (:REWRITE DEFAULT-<-2))
 (736 53 (:REWRITE CONSP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE-IFF))
 (692 505 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (505 505 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (469 469 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (469 469 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (469 469 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (440 22 (:LINEAR <=-OF-0-AND-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (440 22 (:LINEAR <-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-LINEAR))
 (403 28 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (388 205 (:REWRITE DEFAULT-+-2))
 (355 355 (:REWRITE USE-ALL-<-2))
 (355 355 (:REWRITE USE-ALL-<))
 (355 355 (:REWRITE DEFAULT-<-1))
 (340 340 (:REWRITE DEFAULT-CAR))
 (324 18 (:REWRITE EQUAL-OF-LEN-AND-0))
 (322 8 (:REWRITE DARGP-LESS-THAN-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (294 294 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (290 178 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (234 90 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (205 205 (:REWRITE DEFAULT-+-1))
 (200 50 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (195 195 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (174 174 (:REWRITE USE-ALL-<=-2))
 (174 174 (:REWRITE USE-ALL-<=))
 (145 145 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (145 145 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (100 100 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (92 46 (:REWRITE REMOVE-EQUAL-WHEN-NOT-MEMBER-EQUAL-CHEAP))
 (80 40 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (80 8 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (70 35 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (61 61 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (50 50 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (46 46 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (46 46 (:REWRITE REMOVE-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (39 39 (:REWRITE ALL-<-TRANSITIVE))
 (38 18 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (37 37 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (37 37 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (35 35 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (35 35 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (28 28 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (22 2 (:REWRITE ACL2-NUMBERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (18 18 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (18 18 (:LINEAR ARRAY2P-LINEAR))
 (16 8 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (8 8 (:TYPE-PRESCRIPTION MYQUOTEP))
 (8 8 (:REWRITE <=-OF-NTH-WHEN-ALL-<=-FREE))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (2 2 (:TYPE-PRESCRIPTION REMOVE-EQUAL))
 )
(TYPE-OF-SUBSTITUTE-A-VAR-ONE)
(TYPE-OF-SUBSTITUTE-A-VAR-TWO)
(TYPE-OF-SUBSTITUTE-A-VAR-THREE)
(TYPE-OF-SUBSTITUTE-A-VAR-FOUR)
(BOUNDED-DAG-PARENT-ARRAYP-OF-MV-NTH-6-OF-SUBSTITUTE-A-VAR)
(BOUNDED-DAG-DAG-CONSTANT-ALISTP-OF-MV-NTH-7-OF-SUBSTITUTE-A-VAR)
(DAG-DAG-CONSTANT-ALISTP-OF-MV-NTH-7-OF-SUBSTITUTE-A-VAR)
(BOUNDED-DAG-DAG-VARIABLE-ALISTP-OF-MV-NTH-8-OF-SUBSTITUTE-A-VAR)
(NAT-LISTP-OF-MV-NTH-3-OF-SUBSTITUTE-A-VAR
 (3533 870 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (1922 961 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (1266 351 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (1061 158 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (1008 504 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (988 961 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (940 44 (:REWRITE DEFAULT-CDR))
 (904 904 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (821 323 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (760 38 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (702 351 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (610 265 (:REWRITE DEFAULT-<-2))
 (573 330 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (532 41 (:REWRITE CONSP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE-IFF))
 (507 32 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (440 323 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (351 351 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (351 351 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (351 351 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (323 323 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (318 4 (:REWRITE DARGP-LESS-THAN-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (288 16 (:REWRITE EQUAL-OF-LEN-AND-0))
 (280 14 (:LINEAR <=-OF-0-AND-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (280 14 (:LINEAR <-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-LINEAR))
 (272 139 (:REWRITE DEFAULT-+-2))
 (265 265 (:REWRITE USE-ALL-<-2))
 (265 265 (:REWRITE USE-ALL-<))
 (265 265 (:REWRITE DEFAULT-<-1))
 (222 222 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (210 210 (:REWRITE DEFAULT-CAR))
 (190 122 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (178 62 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (155 155 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (139 139 (:REWRITE DEFAULT-+-1))
 (136 34 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (120 120 (:REWRITE USE-ALL-<=-2))
 (120 120 (:REWRITE USE-ALL-<=))
 (118 59 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (97 97 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (97 97 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (68 68 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (53 53 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (52 26 (:REWRITE REMOVE-EQUAL-WHEN-NOT-MEMBER-EQUAL-CHEAP))
 (50 25 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (43 43 (:REWRITE ALL-<-TRANSITIVE))
 (41 41 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (41 41 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (40 4 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (34 34 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (34 14 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (32 32 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (26 26 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (26 26 (:REWRITE REMOVE-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (26 26 (:LINEAR ARRAY2P-LINEAR))
 (25 25 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (25 25 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (22 2 (:REWRITE ACL2-NUMBERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (16 16 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (8 4 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION MYQUOTEP))
 (4 4 (:REWRITE <=-OF-NTH-WHEN-ALL-<=-FREE))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (2 2 (:TYPE-PRESCRIPTION REMOVE-EQUAL))
 )
(TRUE-LISTP-OF-MV-NTH-3-OF-SUBSTITUTE-A-VAR
 (2536 1211 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (1778 298 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (1748 584 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (1648 468 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (1509 1509 (:TYPE-PRESCRIPTION NAT-LISTP))
 (1168 584 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (934 934 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (915 175 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (692 692 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (684 284 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (657 138 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (611 13 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-ALT))
 (584 584 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (568 284 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (559 71 (:REWRITE DEFAULT-+-2))
 (536 169 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (531 23 (:REWRITE DEFAULT-CDR))
 (468 468 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (468 468 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (450 61 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (338 13 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (336 24 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (302 19 (:REWRITE CONSP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE-IFF))
 (299 26 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-BOUNDED-DAG-EXPRP-OF-AREF1))
 (276 138 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (272 175 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (195 26 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (178 69 (:REWRITE DEFAULT-<-2))
 (175 175 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (169 169 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (153 153 (:REWRITE DEFAULT-CAR))
 (144 8 (:REWRITE EQUAL-OF-LEN-AND-0))
 (138 138 (:TYPE-PRESCRIPTION DARGP))
 (138 138 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (138 138 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (138 138 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (122 34 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (120 24 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (104 13 (:REWRITE INTEGERP-OF-NTH-OF-DARGS))
 (103 103 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (99 13 (:REWRITE INTEGERP-OF-NTH-WHEN-ALL-INTEGERP))
 (96 16 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-OF-CAR))
 (91 26 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (78 13 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (76 19 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (71 71 (:REWRITE DEFAULT-+-1))
 (69 69 (:REWRITE USE-ALL-<-2))
 (69 69 (:REWRITE USE-ALL-<))
 (69 69 (:REWRITE DEFAULT-<-1))
 (58 58 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (56 56 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (52 52 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (50 50 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (48 48 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (38 38 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (38 19 (:REWRITE REMOVE-EQUAL-WHEN-NOT-MEMBER-EQUAL-CHEAP))
 (34 13 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (33 33 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (32 32 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (26 26 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (26 26 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (26 26 (:REWRITE DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (26 26 (:REWRITE DAG-EXPRP-WHEN-BOUNDED-DAG-EXPRP))
 (26 13 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (26 13 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (24 24 (:REWRITE USE-ALL-RATIONALP-2))
 (24 24 (:REWRITE USE-ALL-RATIONALP))
 (24 24 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (24 24 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (19 19 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (19 19 (:REWRITE REMOVE-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (19 19 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (19 19 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (16 16 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (16 16 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (16 16 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (13 13 (:TYPE-PRESCRIPTION MYQUOTEP))
 (13 13 (:TYPE-PRESCRIPTION ALL-NATP))
 (13 13 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (13 13 (:REWRITE INTEGERP-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (13 13 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (13 13 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (13 13 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (13 13 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-BETTER))
 (13 13 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-GEN))
 (13 13 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (13 13 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (11 11 (:REWRITE USE-ALL-<=-2))
 (11 11 (:REWRITE USE-ALL-<=))
 (8 8 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(ALL-<-OF-MV-NTH-3-OF-SUBSTITUTE-A-VAR
 (16542 49 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (6747 1686 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (3286 1643 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (2751 399 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (2593 657 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (1899 785 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (1763 1048 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (1670 1643 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (1564 98 (:REWRITE CONSP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE-IFF))
 (1482 1482 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (1416 708 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (1315 61 (:REWRITE DEFAULT-CDR))
 (1314 657 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (1290 590 (:REWRITE DEFAULT-<-2))
 (1206 785 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (980 49 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (785 785 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (770 770 (:REWRITE DEFAULT-CAR))
 (657 657 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (657 657 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (657 657 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (590 590 (:REWRITE USE-ALL-<-2))
 (590 590 (:REWRITE USE-ALL-<))
 (590 590 (:REWRITE DEFAULT-<-1))
 (478 478 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (447 230 (:REWRITE DEFAULT-+-2))
 (440 22 (:LINEAR <=-OF-0-AND-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (440 22 (:LINEAR <-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-LINEAR))
 (396 22 (:REWRITE EQUAL-OF-LEN-AND-0))
 (390 390 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (358 256 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (322 8 (:REWRITE DARGP-LESS-THAN-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (312 129 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (251 251 (:REWRITE USE-ALL-<=-2))
 (251 251 (:REWRITE USE-ALL-<=))
 (230 230 (:REWRITE DEFAULT-+-1))
 (200 50 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (175 175 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (175 175 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (152 76 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (124 62 (:REWRITE REMOVE-EQUAL-WHEN-NOT-MEMBER-EQUAL-CHEAP))
 (118 99 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-MV-NTH-3-OF-SUBSTITUTE-A-VAR))
 (116 2 (:DEFINITION STRIP-CDRS))
 (100 100 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (82 82 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (80 8 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (76 76 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (76 76 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (72 36 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (62 62 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (62 62 (:REWRITE REMOVE-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (61 49 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (60 60 (:REWRITE ALL-<-TRANSITIVE))
 (56 56 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (56 56 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (50 50 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (46 2 (:LINEAR LEN-OF-REMOVE-EQUAL-LINEAR))
 (41 3 (:LINEAR LEN-OF-MV-NTH-2-OF-REBUILD-LITERALS-WITH-SUBSTITUTION))
 (38 18 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (26 26 (:LINEAR ARRAY2P-LINEAR))
 (22 22 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (22 2 (:REWRITE ACL2-NUMBERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (19 19 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (16 8 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (8 8 (:TYPE-PRESCRIPTION REMOVE-EQUAL))
 (8 8 (:TYPE-PRESCRIPTION MYQUOTEP))
 (8 8 (:REWRITE <=-OF-NTH-WHEN-ALL-<=-FREE))
 (8 4 (:REWRITE LEN-OF-REMOVE-EQUAL-WHEN-NO-DUPLICATESP-EQUAL))
 (4 4 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 )
(SUBSTITUTE-VARS
 (225 225 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (224 112 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (220 152 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (185 9 (:REWRITE DEFAULT-CDR))
 (185 9 (:REWRITE DEFAULT-CAR))
 (178 58 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (174 8 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (158 4 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (120 5 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (118 29 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (118 29 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (112 112 (:TYPE-PRESCRIPTION DARGP))
 (112 112 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (112 112 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (112 112 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (100 25 (:REWRITE DEFAULT-*-2))
 (99 50 (:REWRITE DEFAULT-<-2))
 (95 5 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (81 21 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (77 25 (:REWRITE DEFAULT-*-1))
 (66 66 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (64 4 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (53 50 (:REWRITE DEFAULT-<-1))
 (50 50 (:REWRITE USE-ALL-<-2))
 (50 50 (:REWRITE USE-ALL-<))
 (46 16 (:REWRITE DEFAULT-UNARY-/))
 (36 18 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (31 31 (:TYPE-PRESCRIPTION ALL-NATP))
 (26 26 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (24 24 (:REWRITE USE-ALL-<=-2))
 (24 24 (:REWRITE USE-ALL-<=))
 (19 14 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (18 18 (:REWRITE USE-ALL-RATIONALP-2))
 (18 18 (:REWRITE USE-ALL-RATIONALP))
 (18 9 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (12 8 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (11 9 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (10 10 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (10 5 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (10 5 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (8 8 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (8 8 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (8 8 (:LINEAR ARRAY2P-LINEAR))
 (7 7 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (5 5 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (3 3 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 )
(SUBSTITUTE-VARS-RETURN-TYPE
 (8131 80 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (5510 211 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (4655 211 (:REWRITE DEFAULT-CDR))
 (4655 211 (:REWRITE DEFAULT-CAR))
 (4455 211 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (3938 2681 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (3719 3719 (:TYPE-PRESCRIPTION NATP))
 (3704 1852 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (2186 674 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (1852 1852 (:TYPE-PRESCRIPTION DARGP))
 (1852 1852 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (1852 1852 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (1852 1852 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (1648 308 (:REWRITE DEFAULT-UNARY-/))
 (1516 743 (:REWRITE DEFAULT-<-2))
 (1430 337 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (1430 337 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (1364 594 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1162 1162 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (1093 480 (:REWRITE DEFAULT-*-1))
 (1037 480 (:REWRITE DEFAULT-*-2))
 (844 422 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (803 743 (:REWRITE DEFAULT-<-1))
 (777 743 (:REWRITE USE-ALL-<))
 (743 743 (:REWRITE USE-ALL-<-2))
 (519 519 (:REWRITE USE-ALL-RATIONALP-2))
 (519 519 (:REWRITE USE-ALL-RATIONALP))
 (422 422 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (422 211 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (406 406 (:REWRITE USE-ALL-<=-2))
 (406 406 (:REWRITE USE-ALL-<=))
 (337 337 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (294 294 (:LINEAR ARRAY2P-LINEAR))
 (228 158 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (194 82 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (176 88 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (140 10 (:REWRITE NATP-OF-MV-NTH-5-OF-SUBSTITUTE-A-VAR))
 (120 10 (:REWRITE NATP-OF-MV-NTH-1-OF-CRUNCH-DAG-ARRAY2-WITH-INDICES))
 (115 82 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (94 80 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (80 80 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (80 80 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (53 53 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (53 53 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (34 34 (:TYPE-PRESCRIPTION MEMBERP))
 (33 33 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (8 2 (:REWRITE BOUND-ON-MV-NTH-5-OF-SUBSTITUTE-A-VAR-3-GEN))
 )
(SUBSTITUTE-VARS-RETURN-TYPE-COROLLARY
 (78 3 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (69 3 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (21 21 (:TYPE-PRESCRIPTION LEN))
 (17 11 (:REWRITE DEFAULT-<-1))
 (15 11 (:REWRITE USE-ALL-<))
 (14 11 (:REWRITE DEFAULT-<-2))
 (12 6 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (11 11 (:REWRITE USE-ALL-<-2))
 (9 3 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (9 3 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (8 8 (:REWRITE USE-ALL-<=-2))
 (8 8 (:REWRITE USE-ALL-<=))
 (8 4 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (6 3 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (6 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 4 (:TYPE-PRESCRIPTION MEMBERP))
 (4 4 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (3 3 (:TYPE-PRESCRIPTION DARGP))
 (3 3 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (3 3 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (3 3 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (3 3 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (3 3 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (3 3 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (3 3 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-<-TRANSITIVE))
 (3 3 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (2 2 (:REWRITE USE-ALL-RATIONALP-2))
 (2 2 (:REWRITE USE-ALL-RATIONALP))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 )
(SUBSTITUTE-VARS-RETURN-TYPE-2
 (1999 993 (:TYPE-PRESCRIPTION NATP-OF-MV-NTH-5-OF-SUBSTITUTE-A-VAR))
 (1121 24 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (1001 24 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (993 993 (:TYPE-PRESCRIPTION NATP))
 (751 14 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (726 114 (:REWRITE DEFAULT-*-1))
 (605 154 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (590 24 (:REWRITE DEFAULT-CDR))
 (590 24 (:REWRITE DEFAULT-CAR))
 (517 352 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (493 114 (:REWRITE DEFAULT-*-2))
 (484 242 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (307 109 (:REWRITE DEFAULT-<-2))
 (280 80 (:REWRITE DEFAULT-UNARY-/))
 (242 242 (:TYPE-PRESCRIPTION DARGP))
 (242 242 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (242 242 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (242 242 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (228 23 (:REWRITE ALL-<-OF-MV-NTH-5-OF-CRUNCH-DAG-ARRAY2-WITH-INDICES))
 (226 58 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (142 29 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (142 29 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (135 135 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (113 113 (:REWRITE USE-ALL-RATIONALP-2))
 (113 113 (:REWRITE USE-ALL-RATIONALP))
 (109 109 (:REWRITE USE-ALL-<-2))
 (109 109 (:REWRITE USE-ALL-<))
 (109 109 (:REWRITE DEFAULT-<-1))
 (96 48 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (90 24 (:REWRITE NAT-LISTP-OF-MV-NTH-3-OF-SUBSTITUTE-A-VAR))
 (82 82 (:TYPE-PRESCRIPTION WF-DAGP))
 (80 80 (:REWRITE USE-ALL-<=-2))
 (80 80 (:REWRITE USE-ALL-<=))
 (72 72 (:TYPE-PRESCRIPTION ALL-NATP))
 (48 48 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (48 24 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (48 24 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (41 41 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (41 23 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (39 9 (:REWRITE SUBSTITUTE-VARS-RETURN-TYPE))
 (29 29 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (28 14 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (24 24 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (24 8 (:REWRITE TYPE-OF-SUBSTITUTE-A-VAR))
 (23 23 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (14 14 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (14 14 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (9 1 (:REWRITE WF-DAGP-AFTER-CRUNCH-DAG-ARRAY2-WITH-INDICES))
 )
(SUBSTITUTE-VARS-RETURN-TYPE-3
 (3588 101 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (3083 101 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (2425 101 (:REWRITE DEFAULT-CDR))
 (2425 101 (:REWRITE DEFAULT-CAR))
 (2093 57 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (1944 1361 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (1882 941 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (998 233 (:REWRITE DEFAULT-UNARY-/))
 (941 941 (:TYPE-PRESCRIPTION DARGP))
 (941 941 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (941 941 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (941 941 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (870 274 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (769 332 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (763 370 (:REWRITE DEFAULT-<-2))
 (762 369 (:REWRITE DEFAULT-*-1))
 (728 369 (:REWRITE DEFAULT-*-2))
 (684 684 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (572 137 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (572 137 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (549 549 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (404 202 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (370 370 (:REWRITE USE-ALL-<-2))
 (370 370 (:REWRITE USE-ALL-<))
 (370 370 (:REWRITE DEFAULT-<-1))
 (267 267 (:REWRITE USE-ALL-RATIONALP-2))
 (267 267 (:REWRITE USE-ALL-RATIONALP))
 (259 259 (:TYPE-PRESCRIPTION ALL-NATP))
 (233 233 (:REWRITE USE-ALL-<=-2))
 (233 233 (:REWRITE USE-ALL-<=))
 (202 202 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (202 101 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (137 137 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (114 57 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (103 80 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (73 57 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (72 72 (:LINEAR ARRAY2P-LINEAR))
 (61 61 (:REWRITE USE-ALL-NATP-2))
 (61 61 (:REWRITE USE-ALL-NATP))
 (57 57 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (57 57 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (57 57 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (57 57 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (57 57 (:REWRITE ALL-<-TRANSITIVE))
 (42 3 (:REWRITE NATP-OF-MV-NTH-5-OF-SUBSTITUTE-A-VAR))
 (36 3 (:REWRITE NATP-OF-MV-NTH-1-OF-CRUNCH-DAG-ARRAY2-WITH-INDICES))
 )
