X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Ftests%2Fsimpl.ma;h=89812286985c0080428f038b205a8375ed28cd1b;hb=2b2b90087f836c2f32291935216549e9370e68c3;hp=2a860e1906078f25b5ae793d107e7fe0370c169b;hpb=4ac4b8de35d8c4167819acf3d876e69cbd3cfb17;p=helm.git diff --git a/helm/matita/tests/simpl.ma b/helm/matita/tests/simpl.ma index 2a860e190..898122869 100644 --- a/helm/matita/tests/simpl.ma +++ b/helm/matita/tests/simpl.ma @@ -13,36 +13,27 @@ (**************************************************************************) set "baseuri" "cic:/matita/tests/simpl/". -include "coq.ma". +include "legacy/coq.ma". alias symbol "eq" (instance 0) = "Coq's leibnitz's equality". alias id "plus" = "cic:/Coq/Init/Peano/plus.con". alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)". alias id "O" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)". alias id "not" = "cic:/Coq/Init/Logic/not.con". - - -theorem a : - \forall A:Set. - \forall x,y : A. - not (x = y) \to not(y = x). -intros. -simplify. -intro. apply H. -symmetry. -exact H1. -qed. +alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)". +alias id "plus_comm" = "cic:/Coq/Arith/Plus/plus_comm.con". theorem t: let f \def \lambda x,y. x y in f (\lambda x.S x) O = S O. - intros. simplify. change in \vdash (? ? (? %) ?) with O. + intros. simplify. change in \vdash (? ? (? ? %) ?) with O. reflexivity. qed. - + theorem X: \forall x:nat. let myplus \def plus x in myplus (S O) = S x. - intros. simplify. change in \vdash (? ? (% ?) ?) with plus x. - rewrite > plus_comm. reflexivity. qed. - + intros. simplify. change in \vdash (? ? (% ?) ?) with (plus x). + +rewrite > plus_comm. reflexivity. qed. + theorem R: \forall x:nat. let uno \def x + O in S O + uno = 1 + x. intros. simplify. - change in \vdash (? ? (? %) ?) with x + O. + change in \vdash (? ? (? %) ?) with (x + O). rewrite > plus_comm. reflexivity. qed.