X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBase-1%2Fpreamble.ma;h=16ff2dc44be463bdda4863cd1fc716b537a0e211;hb=3b8d99d5fdb79a5d979a8e200a4a4307fe362009;hp=29ebdfeffd222d1c02041af8b02c08fb1ad6b434;hpb=5c1b44dfefa085fbb56e23047652d3650be9d855;p=helm.git diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-1/preamble.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Base-1/preamble.ma index 29ebdfeff..16ff2dc44 100644 --- a/helm/software/matita/contribs/LAMBDA-TYPES/Base-1/preamble.ma +++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-1/preamble.ma @@ -12,101 +12,4 @@ (* *) (**************************************************************************) - - -include "coq.ma". - -alias symbol "eq" = "Coq's leibnitz's equality". -alias symbol "leq" = "Coq's natural 'less or equal to'". -alias symbol "neq" = "Coq's not equal to (leibnitz)". -alias symbol "plus" = "Coq's natural plus". - -alias id "bool" = "cic:/Coq/Init/Datatypes/bool.ind#xpointer(1/1)". -alias id "conj" = "cic:/Coq/Init/Logic/and.ind#xpointer(1/1/1)". -alias id "eq_add_S" = "cic:/Coq/Init/Peano/eq_add_S.con". -alias id "eq" = "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1)". -alias id "eq_ind" = "cic:/Coq/Init/Logic/eq_ind.con". -alias id "eq_ind_r" = "cic:/Coq/Init/Logic/eq_ind_r.con". -alias id "ex2" = "cic:/Coq/Init/Logic/ex2.ind#xpointer(1/1)". -alias id "ex2_ind" = "cic:/Coq/Init/Logic/ex2_ind.con". -alias id "ex_intro2" = "cic:/Coq/Init/Logic/ex2.ind#xpointer(1/1/1)". -alias id "false" = "cic:/Coq/Init/Datatypes/bool.ind#xpointer(1/1/2)". -alias id "False" = "cic:/Coq/Init/Logic/False.ind#xpointer(1/1)". -alias id "False_ind" = "cic:/Coq/Init/Logic/False_ind.con". -alias id "I" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1/1)". -alias id "land" = "cic:/Coq/Init/Logic/and.ind#xpointer(1/1)". -alias id "le" = "cic:/Coq/Init/Peano/le.ind#xpointer(1/1)". -alias id "le_ind" = "cic:/Coq/Init/Peano/le_ind.con". -alias id "le_lt_n_Sm" = "cic:/Coq/Arith/Lt/le_lt_n_Sm.con". -alias id "le_lt_or_eq" = "cic:/Coq/Arith/Lt/le_lt_or_eq.con". -alias id "le_n" = "cic:/Coq/Init/Peano/le.ind#xpointer(1/1/1)". -alias id "le_n_O_eq" = "cic:/Coq/Arith/Le/le_n_O_eq.con". -alias id "le_not_lt" = "cic:/Coq/Arith/Lt/le_not_lt.con". -alias id "le_n_S" = "cic:/Coq/Arith/Le/le_n_S.con". -alias id "le_O_n" = "cic:/Coq/Arith/Le/le_O_n.con". -alias id "le_or_lt" = "cic:/Coq/Arith/Lt/le_or_lt.con". -alias id "le_plus_l" = "cic:/Coq/Arith/Plus/le_plus_l.con". -alias id "le_plus_minus" = "cic:/Coq/Arith/Minus/le_plus_minus.con". -alias id "le_plus_minus_r" = "cic:/Coq/Arith/Minus/le_plus_minus_r.con". -alias id "le_plus_r" = "cic:/Coq/Arith/Plus/le_plus_r.con". -alias id "le_pred_n" = "cic:/Coq/Arith/Le/le_pred_n.con". -alias id "le_S" = "cic:/Coq/Init/Peano/le.ind#xpointer(1/1/2)". -alias id "le_S_n" = "cic:/Coq/Arith/Le/le_S_n.con". -alias id "le_Sn_n" = "cic:/Coq/Arith/Le/le_Sn_n.con". -alias id "le_trans" = "cic:/Coq/Arith/Le/le_trans.con". -alias id "lt" = "cic:/Coq/Init/Peano/lt.con". -alias id "lt_irrefl" = "cic:/Coq/Arith/Lt/lt_irrefl.con". -alias id "lt_le_S" = "cic:/Coq/Arith/Lt/lt_le_S.con". -alias id "lt_n_S" = "cic:/Coq/Arith/Lt/lt_n_S.con". -alias id "minus" = "cic:/Coq/Init/Peano/minus.con". -alias id "minus_n_O" = "cic:/Coq/Arith/Minus/minus_n_O.con". -alias id "minus_plus" = "cic:/Coq/Arith/Minus/minus_plus.con". -alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)". -alias id "nat_ind" = "cic:/Coq/Init/Datatypes/nat_ind.con". -alias id "not" = "cic:/Coq/Init/Logic/not.con". -alias id "not_eq_S" = "cic:/Coq/Init/Peano/not_eq_S.con". -alias id "O" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)". -alias id "or" = "cic:/Coq/Init/Logic/or.ind#xpointer(1/1)". -alias id "or_ind" = "cic:/Coq/Init/Logic/or_ind.con". -alias id "or_introl" = "cic:/Coq/Init/Logic/or.ind#xpointer(1/1/1)". -alias id "or_intror" = "cic:/Coq/Init/Logic/or.ind#xpointer(1/1/2)". -alias id "O_S" = "cic:/Coq/Init/Peano/O_S.con". -alias id "plus_assoc" = "cic:/Coq/Arith/Plus/plus_assoc.con". -alias id "plus_assoc_reverse" = "cic:/Coq/Arith/Plus/plus_assoc_reverse.con". -alias id "plus" = "cic:/Coq/Init/Peano/plus.con". -alias id "plus_comm" = "cic:/Coq/Arith/Plus/plus_comm.con". -alias id "plus_le_compat" = "cic:/Coq/Arith/Plus/plus_le_compat.con". -alias id "plus_le_reg_l" = "cic:/Coq/Arith/Plus/plus_le_reg_l.con". -alias id "plus_lt_reg_l" = "cic:/Coq/Arith/Plus/plus_lt_reg_l.con". -alias id "plus_n_Sm" = "cic:/Coq/Init/Peano/plus_n_Sm.con". -alias id "plus_reg_l" = "cic:/Coq/Arith/Plus/plus_reg_l.con". -alias id "pred" = "cic:/Coq/Init/Peano/pred.con". -alias id "refl_equal" = "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1/1)". -alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)". -alias id "true" = "cic:/Coq/Init/Datatypes/bool.ind#xpointer(1/1/1)". -alias id "True" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1)". - -theorem f_equal: \forall A,B:Type. \forall f:A \to B. - \forall x,y:A. x = y \to f x = f y. - intros. elim H. reflexivity. -qed. - -theorem sym_eq: \forall A:Type. \forall x,y:A. x = y \to y = x. - intros. rewrite > H. reflexivity. -qed. - -theorem sym_not_eq: \forall A:Type. \forall x,y:A. x \neq y \to y \neq x. - unfold not. intros. apply H. symmetry. assumption. -qed. - -theorem trans_eq : \forall A:Type. \forall x,y,z:A. x=y \to y=z \to x=z. - intros. transitivity y; assumption. -qed. - -theorem plus_reg_l: \forall n,m,p. n + m = n + p \to m = p. - intros. apply plus_reg_l; autobatch. -qed. - -theorem plus_le_reg_l: \forall p,n,m. p + n <= p + m \to n <= m. - intros. apply plus_le_reg_l; autobatch. -qed. +include "Legacy-1/theory.ma".