"Coq's " prefix added to every interpretation.

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

diff --git a/helm/matita/tests/fguidi.ma b/helm/matita/tests/fguidi.ma
index 11396b8bdc8160327373a3c5f55037092028b575..07e7989ceb38745e55dca3d61b0a9556f0cd180f 100644 (file)
--- a/helm/matita/tests/fguidi.ma
+++ b/helm/matita/tests/fguidi.ma
@@ -1,4 +1,4 @@
-set "baseuri" "cic:/matita/tests/".
+set "baseuri" "cic:/matita/tests/fguidi/".
 
 alias id "O" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)".
 alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
@@ -7,13 +7,13 @@ 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 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)".
 
+alias symbol "and" (instance 0) = "Coq's logical and".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias symbol "exists" (instance 0) = "Coq's exists".
+
 definition is_S: nat \to Prop \def
    \lambda n. match n with 
       [ O     \Rightarrow False
@@ -53,7 +53,7 @@ qed.
 
 theorem le_gen_x_O_aux: \forall x, y. (le x y) \to (y =O) \to 
                         (x = O).
-intros 3. elim H. auto. apply eq_gen_S_O. exact x2. auto.
+intros 3. elim H. auto. apply eq_gen_S_O. exact n1. auto.
 qed.
 
 theorem le_gen_x_O: \forall x. (le x O) \to (x = O).
@@ -68,7 +68,7 @@ theorem le_gen_S_x_aux: \forall m,x,y. (le y x) \to (y = S m) \to
                         (\exists n. x = (S n) \land (le m n)).
 intros 4. elim H. 
 apply eq_gen_S_O. exact m. elim H1. auto. 
-cut x1 = m. elim Hcut. apply ex_intro. exact x2. auto. auto.
+cut n = m. elim Hcut. apply ex_intro. exact n1. auto. auto.
 qed.
 
 theorem le_gen_S_x: \forall m,x. (le (S m) x) \to 
@@ -82,25 +82,18 @@ 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 left 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; clear H. clear x. 
+auto.
+fwd H1 [H]. decompose H.
+*)