lapply and fwd improved

[helm.git] / helm / matita / tests / fguidi.ma

diff --git a/helm/matita/tests/fguidi.ma b/helm/matita/tests/fguidi.ma
index c0662e78f9986fc3b6d59124efb9272f44aca417..fc2c717eba684ff02a14ef0f1819e8956238d7e0 100644 (file)
--- a/helm/matita/tests/fguidi.ma
+++ b/helm/matita/tests/fguidi.ma
@@ -7,12 +7,12 @@ alias id "le" = "cic:/matita/fguidi/le.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 "ex_intro" = "cic:/Coq/Init/Logic/ex.ind#xpointer(1/1/1)".
+alias id "False" = "cic:/Coq/Init/Logic/False.ind#xpointer(1/1)".
+alias id "True" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1)".
 
 alias symbol "and" (instance 0) = "logical and".
 alias symbol "eq" (instance 0) = "leibnitz's equality".
 alias symbol "exists" (instance 0) = "exists".
-alias id "False" = "cic:/Coq/Init/Logic/False.ind#xpointer(1/1)".
-alias id "True" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1)".
 
 definition is_S: nat \to Prop \def
    \lambda n. match n with 
@@ -82,25 +82,17 @@ intros. elim H. elim H1. cut (S x1) = x. elim Hcut. auto. elim H2. auto.
 qed.
 
 theorem le_gen_S_S: \forall m,n. (le (S m) (S n)) \to (le m n).
-intros. cut (\exists p. (S n) = (S p) \land (le m p)).
-elim Hcut. elim H1. cut x = n. 
-elim Hcut1. auto. symmetry. auto. auto.
+intros.
+lapply le_gen_S_x to H using H0. elim H0. elim H1. 
+lapply eq_gen_S_S to H2 using H4. rewrite > H4. assumption.
 qed.
 
 theorem le_gen_S_S_cc: \forall m,n. (le m n) \to (le (S m) (S n)).
 intros. auto.
 qed.
-
-theorem le_gen_S_x_2: \forall m,x. (le (S m) x) \to
-                        \exists n. x = (S n) \land (le m n).
-intros.
-lapply le_gen_S_x to H using H0. elim H0. elim H1.
-exists. exact x1. auto.
-qed.
-
-(* proof of le_gen_S_S with lapply *)
-theorem le_gen_S_S_2: \forall m,n. (le (S m) (S n)) \to (le m n).
-intros.
-lapply le_gen_S_x_2 to H using H0. elim H0. elim H1. 
-lapply eq_gen_S_S to H2 using H4. rewrite > H4. assumption.
-qed.
+(*
+theorem le_trans: \forall x,y. (le x y) \to \forall z. (le y z) \to (le x z).
+intros 1.
+elim x. auto.
+fwd H1 [].
+*)