(**************************************************************************)
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.