(FUNPOL::CLOSURE-LAWS)
(FUNPOL::EQUIVALENCE-LAW)
(FUNPOL::CONGRUENCE-LAWS)
(FUNPOL::CLOSURE-OF-C_=)
(FUNPOL::EQUIVALENCE-CLASS-LAWS
 (19 2 (:DEFINITION FUPOL::POLINOMIOP))
 (15 3 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (13 1 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (11 11 (:REWRITE DEFAULT-CDR))
 (11 3 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (8 8 (:REWRITE DEFAULT-CAR))
 (6 6 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (6 6 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (6 2 (:REWRITE FUNPOL::|not FUMON::nulop (primero p)|))
 (6 2 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (4 2 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (3 3 (:REWRITE FUTER::|a < b & b < c => a < c|))
 )
(FUNPOL::COMMUTATIVITY-LAWS
 (163 3 (:REWRITE FUNPOL::|p + q = mp(q) +Mo (p + (resto(q))|))
 (134 12 (:DEFINITION FUPOL::POLINOMIOP))
 (85 3 (:REWRITE FUNPOL::|p + q = mp(p) +Mo (resto(p) + q)|))
 (85 3 (:REWRITE FUNPOL::|p + q = mp(p) +Mo (mp(q) +Mo (resto(p) + (resto q)))|))
 (70 14 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (62 62 (:REWRITE DEFAULT-CDR))
 (48 48 (:REWRITE DEFAULT-CAR))
 (40 20 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (38 14 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (28 28 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (28 28 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (28 12 (:REWRITE FUNPOL::|not FUMON::nulop (primero p)|))
 (28 12 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (26 2 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (14 14 (:REWRITE FUTER::|a < b & b < c => a < c|))
 )
(FUNPOL::ASSOCIATIVITY-LAWS)
(FUNPOL::LEFT-DISTRIBUTIVITY-LAW
 (287 3 (:REWRITE FUNPOL::|p + q = mp(q) +Mo (p + (resto(q))|))
 (255 19 (:DEFINITION FUPOL::POLINOMIOP))
 (243 3 (:REWRITE FUNPOL::|p1 * p2 = 0 <=> p1 = 0 or p2 = 0|))
 (187 3 (:REWRITE FUNPOL::|p + q = mp(p) +Mo (resto(p) + q)|))
 (187 3 (:REWRITE FUNPOL::|p + q = mp(p) +Mo (mp(q) +Mo (resto(p) + (resto q)))|))
 (126 18 (:REWRITE FUNPOL::|primero (p1 * p2) =e (primero p1) FUMON::* (primero p2)|))
 (110 22 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (98 98 (:REWRITE DEFAULT-CDR))
 (76 76 (:REWRITE DEFAULT-CAR))
 (64 32 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (59 22 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (44 44 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (44 44 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (44 19 (:REWRITE FUNPOL::|not FUMON::nulop (primero p)|))
 (44 19 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (39 3 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (22 22 (:REWRITE FUTER::|a < b & b < c => a < c|))
 (18 18 (:TYPE-PRESCRIPTION ATOM))
 (18 18 (:DEFINITION ATOM))
 )
(FUNPOL::LEFT-UNICITY-LAWS
 (52 7 (:DEFINITION FUPOL::POLINOMIOP))
 (49 1 (:REWRITE FUNPOL::|p + q = mp(q) +Mo (p + (resto(q))|))
 (25 5 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (21 21 (:REWRITE DEFAULT-CDR))
 (16 16 (:REWRITE DEFAULT-CAR))
 (15 5 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (13 1 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (12 12 (:TYPE-PRESCRIPTION FUNPOL::NULO))
 (12 6 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (10 10 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (10 10 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (10 4 (:REWRITE FUNPOL::|not FUMON::nulop (primero p)|))
 (10 4 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (10 1 (:REWRITE FUNPOL::|p + q = mp(p) +Mo (resto(p) + q)|))
 (10 1 (:REWRITE FUNPOL::|p + q = mp(p) +Mo (mp(q) +Mo (resto(p) + (resto q)))|))
 (5 5 (:REWRITE FUTER::|a < b & b < c => a < c|))
 )
(FUNPOL::RIGHT-INVERSE-LAW)
(FUNPOL::ZERO-DIVISOR-LAW
 (38 4 (:DEFINITION FUPOL::POLINOMIOP))
 (30 6 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (26 2 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (22 22 (:REWRITE DEFAULT-CDR))
 (22 6 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (16 16 (:REWRITE DEFAULT-CAR))
 (12 12 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (12 12 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (12 4 (:REWRITE FUNPOL::|not FUMON::nulop (primero p)|))
 (12 4 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (8 4 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (6 6 (:REWRITE FUTER::|a < b & b < c => a < c|))
 )
(FUNPOL::NATP-DEG-SIZE)
(FUNPOL::CONGRUENCE-FOR-DEG
 (96 48 (:TYPE-PRESCRIPTION FUNPOL::NATP-DEG))
 (30 3 (:DEFINITION FUPOL::POLINOMIOP))
 (27 2 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (25 5 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (24 5 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (18 18 (:REWRITE DEFAULT-CDR))
 (14 3 (:REWRITE FUNPOL::|not FUMON::nulop (primero p)|))
 (14 3 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (12 12 (:REWRITE DEFAULT-CAR))
 (10 10 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (10 10 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (5 5 (:REWRITE FUTER::|a < b & b < c => a < c|))
 (4 2 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 )
(FUNPOL::CLOSURE-OF-QUOT-&-REM)
(FUNPOL::CONGRUENCE-FOR-QUOT-&-REM)
(FUNPOL::DIVISION-PROPERTY
 (75075 17 (:DEFINITION FUNPOL::QUOT))
 (54911 17 (:DEFINITION FUPOL::+-MONOMIO))
 (44145 121 (:REWRITE FUNPOL::|p1 = 0 => quot(p1 p2) =e 0|))
 (35696 145 (:REWRITE FUNPOL::|p + q = mp(q) +Mo (p + (resto(q))|))
 (34502 1206 (:DEFINITION FUPOL::POLINOMIOP))
 (30075 145 (:REWRITE FUNPOL::|p + q = mp(p) +Mo (resto(p) + q)|))
 (30075 145 (:REWRITE FUNPOL::|p + q = mp(p) +Mo (mp(q) +Mo (resto(p) + (resto q)))|))
 (25855 923 (:DEFINITION FUPOL::*-MONOMIO))
 (24999 2049 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (19275 79 (:REWRITE FUNPOL::|p + q = 0 <=> q = - p|))
 (16495 17 (:DEFINITION FUMON::+))
 (16479 17 (:REWRITE FUMON::=-IMPLIES-EQUAL-TERMINO-2))
 (16393 17 (:REWRITE FLD::|a + b = b + a|))
 (15216 991 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (13849 190 (:REWRITE FUNPOL::|resto -p = - resto p|))
 (12780 2 (:REWRITE FUNPOL::|p1 * p2 = 0 <=> p1 = 0 or p2 = 0|))
 (10332 843 (:REWRITE FUMON::|a * b = b * a|))
 (9686 121 (:REWRITE FUNPOL::|deg p1 < deq p2 => quot(p1 p2) =e 0|))
 (8607 376 (:REWRITE FUPOL::|ordenadop p => ordenadop m *M p|))
 (8154 9 (:REWRITE FUNPOL::|primero (p1 * p2) =e (primero p1) FUMON::* (primero p2)|))
 (5972 5972 (:REWRITE DEFAULT-CDR))
 (5765 63 (:REWRITE FUNPOL::|- p != 0|))
 (5298 1008 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (5051 67 (:REWRITE FUNPOL::|FUMON::termino (primero (- p)) =e FUMON::termino FUMON::- (primero p)|))
 (5038 5038 (:REWRITE DEFAULT-CAR))
 (4255 121 (:REWRITE FUNPOL::|~(polinomiop p1) => quot(p1 p2) =e 0|))
 (3747 56 (:REWRITE FUNPOL::|primero -p FUMON::= FUMON::- primero p|))
 (3734 410 (:REWRITE FUNPOL::|not FUMON::nulop m|))
 (2972 376 (:REWRITE FUNPOL::|polinomiop (m FUPOL::*-monomio p2)|))
 (2947 957 (:REWRITE DEFAULT-+-1))
 (2820 940 (:REWRITE FUNPOL::|deg (quot p1 p2) =e deg(p1) ACL2::- deg(p2)-lemma-3|))
 (2273 46 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (2202 488 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2145 2145 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (2145 2145 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (2083 427 (:REWRITE FUMON::COEFICIENTE-MONOMIO))
 (2017 91 (:REWRITE DEFAULT-<-1))
 (1944 1038 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (1914 957 (:REWRITE DEFAULT-UNARY-MINUS))
 (1914 957 (:REWRITE DEFAULT-+-2))
 (1883 236 (:REWRITE FUNPOL::|m FUPOL::*-monomio p2 != 0|))
 (1880 914 (:REWRITE FUNPOL::|not FUMON::nulop (primero p)|))
 (1870 1870 (:TYPE-PRESCRIPTION FLD::BOOLEANP-FDP))
 (1581 63 (:REWRITE FUNPOL::|deg(p + q) =_e deg(q)|))
 (1581 63 (:REWRITE FUNPOL::|deg(p + q) =_e deg(p)|))
 (1581 63 (:LINEAR FUNPOL::|deg(p + q) ACL2::< deg(p)-a|))
 (1581 63 (:LINEAR FUNPOL::|deg(p + q) ACL2::< deg(p)|))
 (1407 63 (:REWRITE FUNPOL::|- (m FUPOL::*-monomio p2) != 0|))
 (1388 694 (:TYPE-PRESCRIPTION FLD::FDP-*))
 (1230 410 (:REWRITE FUNPOL::|deg (quot p1 p2) =e deg(p1) ACL2::- deg(p2)-lemma-4|))
 (1230 246 (:TYPE-PRESCRIPTION FUMON::MONOMIOP-MONOMIO))
 (1008 1008 (:REWRITE FUTER::|a < b & b < c => a < c|))
 (711 17 (:REWRITE FUMON::=-IMPLIES-EQUAL-TERMINO-1))
 (647 647 (:TYPE-PRESCRIPTION FUNPOL::POLINOMIOP-+))
 (376 376 (:TYPE-PRESCRIPTION FUMON::NULOP))
 (348 12 (:REWRITE FUNPOL::|nil + p = p|))
 (324 10 (:DEFINITION FUPOL::>-MONOMIO))
 (280 56 (:REWRITE FUNPOL::|primero (- (m *-monomio p2)) = - (primero (m *-monomio p2))|))
 (208 121 (:REWRITE FUNPOL::|~(polinomiop p2) => quot(p1 p2) =e 0|))
 (182 91 (:REWRITE DEFAULT-<-2))
 (170 34 (:REWRITE FUMON::TERMINO-MONOMIO))
 (142 142 (:TYPE-PRESCRIPTION FUNPOL::POLINOMIOP--))
 (130 4 (:REWRITE FUNPOL::|(polinomiop p1) & ~(polinomiop p2) => rem(p1 p2) = p1|))
 (123 121 (:REWRITE FUNPOL::|p2 = 0 => quot(p1 p2) =e 0|))
 (120 24 (:REWRITE FUNPOL::|deg(p + q) =_e deg(p)-lema-4|))
 (102 34 (:REWRITE FUNPOL::|deg (quot p1 p2) =e deg(p1) ACL2::- deg(p2)-lemma-5|))
 (68 30 (:REWRITE FUPOL::|m FUMON::> n and n >-monomio p => m >-monomio p|))
 (58 4 (:REWRITE FUNPOL::|(polinomiop p1) & deg p1 < deq p2 => rem(p1 p2) = p1|))
 (53 53 (:REWRITE FUNPOL::=-IMPLIES-=-QUOT-2-LEMMA-1))
 (53 53 (:REWRITE FUNPOL::=-IMPLIES-=-QUOT-1-LEMMA-1))
 (48 48 (:TYPE-PRESCRIPTION FUPOL::*-MONOMIO))
 (45 4 (:REWRITE FUNPOL::|(polinomiop p1) & p2 = 0 => rem(p1 p2) = 0|))
 (40 40 (:TYPE-PRESCRIPTION FUPOL::>-MONOMIO))
 (38 10 (:REWRITE FUPOL::|primero p FUMON::< m => >-monomio m p|))
 (29 29 (:REWRITE FUNPOL::POLINOMIOP-QUOT))
 (28 10 (:REWRITE FUPOL::|ordenadop p => (primero p) >-monomio (resto p)|))
 (17 17 (:TYPE-PRESCRIPTION FUMON::COEFICIENTEP-COEFICIENTE))
 (12 12 (:REWRITE FUPOL::POLINOMIOP-*-MONOMIO))
 (12 12 (:REWRITE FUNPOL::|- nil =e nil|))
 (9 9 (:TYPE-PRESCRIPTION ATOM))
 (9 9 (:DEFINITION ATOM))
 (6 4 (:REWRITE FUNPOL::|p1 = 0 => rem(p1 p2) = 0|))
 (3 3 (:TYPE-PRESCRIPTION FUNPOL::POLINOMIOP-*))
 (1 1 (:REWRITE FUNPOL::POLINOMIOP-REM))
 )
(FUNPOL::DEG-*
 (134 12 (:DEFINITION FUPOL::POLINOMIOP))
 (70 14 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (62 62 (:REWRITE DEFAULT-CDR))
 (48 48 (:REWRITE DEFAULT-CAR))
 (46 46 (:TYPE-PRESCRIPTION FUNPOL::POLINOMIOP-*))
 (40 20 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (38 14 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (28 28 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (28 28 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (28 12 (:REWRITE FUNPOL::|not FUMON::nulop (primero p)|))
 (28 12 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (26 2 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (14 14 (:REWRITE FUTER::|a < b & b < c => a < c|))
 (6 3 (:REWRITE DEFAULT-+-2))
 (6 3 (:REWRITE DEFAULT-+-1))
 (3 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-<-2))
 )
(FUNPOL::DIVIDES-P)
(FUNPOL::DIVIDES-P-SUFF)
(FUNPOL::UNIT-P)
(FUNPOL::|deg identidad =e 0|
 (4 4 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(FUNPOL::DEG-UNIT-P=0
 (75075 17 (:DEFINITION FUNPOL::QUOT))
 (54911 17 (:DEFINITION FUPOL::+-MONOMIO))
 (44145 121 (:REWRITE FUNPOL::|p1 = 0 => quot(p1 p2) =e 0|))
 (36195 152 (:REWRITE FUNPOL::|p + q = mp(q) +Mo (p + (resto(q))|))
 (35218 1272 (:DEFINITION FUPOL::POLINOMIOP))
 (30357 152 (:REWRITE FUNPOL::|p + q = mp(p) +Mo (resto(p) + q)|))
 (30357 152 (:REWRITE FUNPOL::|p + q = mp(p) +Mo (mp(q) +Mo (resto(p) + (resto q)))|))
 (25855 923 (:DEFINITION FUPOL::*-MONOMIO))
 (25167 2112 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (19275 79 (:REWRITE FUNPOL::|p + q = 0 <=> q = - p|))
 (16495 17 (:DEFINITION FUMON::+))
 (16479 17 (:REWRITE FUMON::=-IMPLIES-EQUAL-TERMINO-2))
 (16393 17 (:REWRITE FLD::|a + b = b + a|))
 (15479 1073 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (13849 190 (:REWRITE FUNPOL::|resto -p = - resto p|))
 (10332 843 (:REWRITE FUMON::|a * b = b * a|))
 (9686 121 (:REWRITE FUNPOL::|deg p1 < deq p2 => quot(p1 p2) =e 0|))
 (8607 376 (:REWRITE FUPOL::|ordenadop p => ordenadop m *M p|))
 (8280 27 (:REWRITE FUNPOL::|primero (p1 * p2) =e (primero p1) FUMON::* (primero p2)|))
 (6307 6307 (:REWRITE DEFAULT-CDR))
 (5765 63 (:REWRITE FUNPOL::|- p != 0|))
 (5708 1090 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (5290 5290 (:REWRITE DEFAULT-CAR))
 (5051 67 (:REWRITE FUNPOL::|FUMON::termino (primero (- p)) =e FUMON::termino FUMON::- (primero p)|))
 (4255 121 (:REWRITE FUNPOL::|~(polinomiop p1) => quot(p1 p2) =e 0|))
 (3747 56 (:REWRITE FUNPOL::|primero -p FUMON::= FUMON::- primero p|))
 (3734 410 (:REWRITE FUNPOL::|not FUMON::nulop m|))
 (2972 376 (:REWRITE FUNPOL::|polinomiop (m FUPOL::*-monomio p2)|))
 (2953 960 (:REWRITE DEFAULT-+-1))
 (2820 940 (:REWRITE FUNPOL::|deg (quot p1 p2) =e deg(p1) ACL2::- deg(p2)-lemma-3|))
 (2521 65 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (2309 2309 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (2309 2309 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (2202 488 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2120 1126 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (2083 427 (:REWRITE FUMON::COEFICIENTE-MONOMIO))
 (2048 977 (:REWRITE FUNPOL::|not FUMON::nulop (primero p)|))
 (2020 92 (:REWRITE DEFAULT-<-1))
 (1920 960 (:REWRITE DEFAULT-+-2))
 (1914 957 (:REWRITE DEFAULT-UNARY-MINUS))
 (1883 236 (:REWRITE FUNPOL::|m FUPOL::*-monomio p2 != 0|))
 (1870 1870 (:TYPE-PRESCRIPTION FLD::BOOLEANP-FDP))
 (1581 63 (:REWRITE FUNPOL::|deg(p + q) =_e deg(q)|))
 (1581 63 (:REWRITE FUNPOL::|deg(p + q) =_e deg(p)|))
 (1581 63 (:LINEAR FUNPOL::|deg(p + q) ACL2::< deg(p)-a|))
 (1581 63 (:LINEAR FUNPOL::|deg(p + q) ACL2::< deg(p)|))
 (1407 63 (:REWRITE FUNPOL::|- (m FUPOL::*-monomio p2) != 0|))
 (1388 694 (:TYPE-PRESCRIPTION FLD::FDP-*))
 (1230 410 (:REWRITE FUNPOL::|deg (quot p1 p2) =e deg(p1) ACL2::- deg(p2)-lemma-4|))
 (1230 246 (:TYPE-PRESCRIPTION FUMON::MONOMIOP-MONOMIO))
 (1090 1090 (:REWRITE FUTER::|a < b & b < c => a < c|))
 (711 17 (:REWRITE FUMON::=-IMPLIES-EQUAL-TERMINO-1))
 (376 376 (:TYPE-PRESCRIPTION FUMON::NULOP))
 (348 12 (:REWRITE FUNPOL::|nil + p = p|))
 (324 10 (:DEFINITION FUPOL::>-MONOMIO))
 (280 56 (:REWRITE FUNPOL::|primero (- (m *-monomio p2)) = - (primero (m *-monomio p2))|))
 (208 121 (:REWRITE FUNPOL::|~(polinomiop p2) => quot(p1 p2) =e 0|))
 (184 92 (:REWRITE DEFAULT-<-2))
 (170 34 (:REWRITE FUMON::TERMINO-MONOMIO))
 (130 4 (:REWRITE FUNPOL::|(polinomiop p1) & ~(polinomiop p2) => rem(p1 p2) = p1|))
 (123 121 (:REWRITE FUNPOL::|p2 = 0 => quot(p1 p2) =e 0|))
 (120 24 (:REWRITE FUNPOL::|deg(p + q) =_e deg(p)-lema-4|))
 (102 34 (:REWRITE FUNPOL::|deg (quot p1 p2) =e deg(p1) ACL2::- deg(p2)-lemma-5|))
 (68 30 (:REWRITE FUPOL::|m FUMON::> n and n >-monomio p => m >-monomio p|))
 (58 4 (:REWRITE FUNPOL::|(polinomiop p1) & deg p1 < deq p2 => rem(p1 p2) = p1|))
 (53 53 (:REWRITE FUNPOL::=-IMPLIES-=-QUOT-2-LEMMA-1))
 (53 53 (:REWRITE FUNPOL::=-IMPLIES-=-QUOT-1-LEMMA-1))
 (48 48 (:TYPE-PRESCRIPTION FUPOL::*-MONOMIO))
 (45 4 (:REWRITE FUNPOL::|(polinomiop p1) & p2 = 0 => rem(p1 p2) = 0|))
 (40 40 (:TYPE-PRESCRIPTION FUPOL::>-MONOMIO))
 (38 10 (:REWRITE FUPOL::|primero p FUMON::< m => >-monomio m p|))
 (28 10 (:REWRITE FUPOL::|ordenadop p => (primero p) >-monomio (resto p)|))
 (27 27 (:TYPE-PRESCRIPTION ATOM))
 (27 27 (:DEFINITION ATOM))
 (17 17 (:TYPE-PRESCRIPTION FUMON::COEFICIENTEP-COEFICIENTE))
 (12 12 (:TYPE-PRESCRIPTION FUNPOL::NULO))
 (12 12 (:REWRITE FUPOL::POLINOMIOP-*-MONOMIO))
 (12 12 (:REWRITE FUNPOL::|- nil =e nil|))
 (6 4 (:REWRITE FUNPOL::|p1 = 0 => rem(p1 p2) = 0|))
 )
(FUNPOL::DEG=0-IMPLIES-UNIT-P)
(FUNPOL::DEG-<-DEG-*
 (237 9 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (225 36 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (210 21 (:DEFINITION FUPOL::POLINOMIOP))
 (168 36 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (117 117 (:REWRITE DEFAULT-CDR))
 (99 3 (:DEFINITION FUPOL::>-MONOMIO))
 (87 87 (:REWRITE DEFAULT-CAR))
 (80 80 (:TYPE-PRESCRIPTION FUNPOL::POLINOMIOP-*))
 (66 66 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (66 66 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (63 21 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (48 24 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (36 36 (:REWRITE FUTER::|a < b & b < c => a < c|))
 (21 9 (:REWRITE FUPOL::|m FUMON::> n and n >-monomio p => m >-monomio p|))
 (12 12 (:TYPE-PRESCRIPTION FUPOL::>-MONOMIO))
 (12 3 (:REWRITE FUPOL::|primero p FUMON::< m => >-monomio m p|))
 (9 3 (:REWRITE FUPOL::|ordenadop p => (primero p) >-monomio (resto p)|))
 (8 4 (:REWRITE DEFAULT-+-1))
 (6 4 (:REWRITE DEFAULT-+-2))
 (4 2 (:REWRITE DEFAULT-<-2))
 (4 2 (:REWRITE DEFAULT-<-1))
 )
(FUNPOL::REDUCIBLE-P)
(FUNPOL::REDUCIBLE-P-SUFF
 (4 4 (:DEFINITION MV-NTH))
 )
(FUNPOL::IRREDUCIBLE-P)
(FUNPOL::IRREDUCIBLE-P-IMPLIES-PRIME-PROPERTY
 (861 62 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (713 62 (:DEFINITION FUPOL::POLINOMIOP))
 (641 124 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (620 124 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (436 436 (:REWRITE DEFAULT-CDR))
 (303 62 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (268 268 (:REWRITE DEFAULT-CAR))
 (248 248 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (248 248 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (165 30 (:REWRITE FUNPOL::|not FUMON::nulop (primero p)|))
 (159 29 (:REWRITE FUNPOL::DIVIDES-P-SUFF))
 (128 64 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (124 124 (:REWRITE FUTER::|a < b & b < c => a < c|))
 )
(FUNPOL::IRREDUCIBLE-FACTORS
 (1531 89 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (1195 208 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (1000 208 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (594 594 (:REWRITE DEFAULT-CDR))
 (408 10 (:REWRITE FUNPOL::|deg (p1 * p2) =e deg p1 ACL2::+ deg p2|))
 (406 406 (:REWRITE DEFAULT-CAR))
 (396 396 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (396 396 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (360 99 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (330 10 (:DEFINITION FUPOL::>-MONOMIO))
 (208 208 (:REWRITE FUTER::|a < b & b < c => a < c|))
 (70 30 (:REWRITE FUPOL::|m FUMON::> n and n >-monomio p => m >-monomio p|))
 (60 60 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP))
 (60 20 (:REWRITE FUNPOL::REDUCIBLE-P-SUFF))
 (54 4 (:REWRITE DEFAULT-<-2))
 (40 40 (:TYPE-PRESCRIPTION FUPOL::>-MONOMIO))
 (40 20 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (40 10 (:REWRITE FUPOL::|primero p FUMON::< m => >-monomio m p|))
 (40 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (32 4 (:REWRITE DEFAULT-<-1))
 (30 10 (:REWRITE FUPOL::|ordenadop p => (primero p) >-monomio (resto p)|))
 (10 10 (:EQUIVALENCE FLD::EQUIVALENCE-LAW))
 (1 1 (:TYPE-PRESCRIPTION TRUE-LISTP))
 )
(FUNPOL::POLINOMIOP-LISTP)
(FUNPOL::IRREDUCIBLE-LISTP)
(FUNPOL::*-LST)
(FUNPOL::IRREDUCIBLE-FACTORIZATION-EXISTENCE
 (4878 12 (:REWRITE FUNPOL::REDUCIBLE-P-SUFF))
 (4836 30 (:DEFINITION FUNPOL::UNIT-P))
 (4710 30 (:DEFINITION FUNPOL::DIVIDES-P))
 (2506 86 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (2176 236 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (1120 32 (:DEFINITION FUPOL::>-MONOMIO))
 (1098 86 (:DEFINITION FUPOL::POLINOMIOP))
 (1052 236 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (590 590 (:REWRITE DEFAULT-CDR))
 (447 447 (:REWRITE DEFAULT-CAR))
 (420 86 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (408 408 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (408 408 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (240 120 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (236 236 (:REWRITE FUTER::|a < b & b < c => a < c|))
 (224 96 (:REWRITE FUPOL::|m FUMON::> n and n >-monomio p => m >-monomio p|))
 (128 128 (:TYPE-PRESCRIPTION FUPOL::>-MONOMIO))
 (128 32 (:REWRITE FUPOL::|primero p FUMON::< m => >-monomio m p|))
 (96 32 (:REWRITE FUPOL::|ordenadop p => (primero p) >-monomio (resto p)|))
 (96 30 (:REWRITE FUNPOL::DIVIDES-P-SUFF))
 (60 60 (:EQUIVALENCE FLD::EQUIVALENCE-LAW))
 (55 11 (:DEFINITION BINARY-APPEND))
 (30 30 (:TYPE-PRESCRIPTION FUNPOL::UNIT-P))
 (6 6 (:REWRITE FUNPOL::|p * q = q * p|))
 )
(FUNPOL::UNIT-ASSOCIATES-P)
(FUNPOL::UNIT-ASSOCIATES-P-SUFF)
(FUNPOL::IRREDUCIBLE-P-UNIT-ASSOCIATES
 (436 10 (:DEFINITION FUPOL::ORDENADOP))
 (104 8 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (90 18 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (82 2 (:REWRITE FUNPOL::DIVIDES-P-SUFF))
 (80 10 (:DEFINITION FUPOL::POLINOMIOP))
 (76 18 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (58 58 (:REWRITE DEFAULT-CDR))
 (40 40 (:REWRITE DEFAULT-CAR))
 (36 36 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (36 36 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (36 10 (:REWRITE FUNPOL::|not FUMON::nulop (primero p)|))
 (36 10 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (28 28 (:TYPE-PRESCRIPTION FUTER::<))
 (18 18 (:REWRITE FUTER::|a < b & b < c => a < c|))
 (12 12 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP))
 (12 10 (:DEFINITION FUMON::NULOP))
 (8 4 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (2 2 (:EQUIVALENCE FLD::EQUIVALENCE-LAW))
 (1 1 (:REWRITE FUNPOL::UNIT-ASSOCIATES-P-SUFF))
 )
(FUNPOL::MEMBER-UNIT-ASSOCIATE)
(FUNPOL::DELETE-ONE-UNIT-ASSOCIATE)
(FUNPOL::BAG-EQUAL-UNIT-ASSOCIATES)
(FUNPOL::BAG-EQUAL-UNIT-ASSOCIATES->EQUAL-LEN
 (4956 98 (:DEFINITION FUPOL::ORDENADOP))
 (1208 80 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (1092 178 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (944 98 (:DEFINITION FUPOL::POLINOMIOP))
 (904 904 (:REWRITE DEFAULT-CAR))
 (890 178 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (749 749 (:REWRITE DEFAULT-CDR))
 (738 18 (:REWRITE FUNPOL::DIVIDES-P-SUFF))
 (524 98 (:REWRITE FUNPOL::|not FUMON::nulop (primero p)|))
 (524 98 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (356 356 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (356 356 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (276 276 (:TYPE-PRESCRIPTION FUTER::<))
 (178 178 (:REWRITE FUTER::|a < b & b < c => a < c|))
 (116 98 (:DEFINITION FUMON::NULOP))
 (108 108 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP))
 (72 36 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (42 42 (:REWRITE FUNPOL::UNIT-ASSOCIATES-P-SUFF))
 (18 18 (:EQUIVALENCE FLD::EQUIVALENCE-LAW))
 )
(FUNPOL::BAG-EQUAL-UNIT-ASSOCIATES->IFF-MEMBER-UNIT-ASSOCIATE)
(FUNPOL::MULTIPLICITY-UNIT-ASSOCIATE)
(FUNPOL::BAG-EQUAL-UNIT-ASSOCIATES->EQUAL-MULTIPLICITY-UNIT-ASSOCIATE
 (1620 34 (:DEFINITION FUPOL::ORDENADOP))
 (397 28 (:REWRITE FUTER::|a < b => ~(b < a)|))
 (330 62 (:REWRITE FUNPOL::|deg(p + q) ACL2::< deg(p)-lemma-5|))
 (310 62 (:REWRITE FUTER::|a < b or b < a or a = b|))
 (301 34 (:DEFINITION FUPOL::POLINOMIOP))
 (260 260 (:REWRITE DEFAULT-CDR))
 (246 6 (:REWRITE FUNPOL::DIVIDES-P-SUFF))
 (235 235 (:REWRITE DEFAULT-CAR))
 (157 34 (:REWRITE FUNPOL::|not FUMON::nulop (primero p)|))
 (157 34 (:REWRITE FUNPOL::|FUMON::monomiop (primero p)|))
 (124 124 (:TYPE-PRESCRIPTION FUMON::TERMINOP-TERMINO))
 (124 124 (:TYPE-PRESCRIPTION FUTER::BOOLEANP-TERMINOP))
 (96 96 (:TYPE-PRESCRIPTION FUTER::<))
 (62 62 (:REWRITE FUTER::|a < b & b < c => a < c|))
 (40 34 (:DEFINITION FUMON::NULOP))
 (36 36 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP))
 (24 12 (:TYPE-PRESCRIPTION FUPOL::POLINOMIOP-RESTO))
 (14 7 (:REWRITE DEFAULT-+-2))
 (7 7 (:REWRITE DEFAULT-+-1))
 (6 6 (:REWRITE FUNPOL::UNIT-ASSOCIATES-P-SUFF))
 (6 6 (:EQUIVALENCE FLD::EQUIVALENCE-LAW))
 )
(FUNPOL::IRREDUCIBLE-FACTORIZATION-UNIQUENESS-GENERAL)
(FUNPOL::IRREDUCIBLE-FACTORIZATION-UNIQUENESS)
