claudio, please have a look at this

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

diff --git a/helm/software/matita/tests/fguidi.ma b/helm/software/matita/tests/fguidi.ma
index fab765baff7f2b4de9621ff67aa509190a793fdf..c0aa6b2840aa22d6b016a25f847835411bc5886d 100644 (file)
--- a/helm/software/matita/tests/fguidi.ma
+++ b/helm/software/matita/tests/fguidi.ma
@@ -12,50 +12,11 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/tests/fguidi/".
-include "legacy/coq.ma".
+include "logic/connectives.ma".
+include "nat/nat.ma".
 
-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)".
-alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
-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) = "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
-      | (S n) \Rightarrow True
-      ].
-
-definition pred: nat \to nat \def
-   \lambda n. match n with
-      [ O     \Rightarrow O
-      | (S n) \Rightarrow n
-      ]. 
-
-theorem eq_gen_S_O: \forall x. (S x = O) \to \forall P:Prop. P.
-intros. apply False_ind. cut (is_S O). auto new. elim H. exact I.
-qed.
-
-theorem eq_gen_S_O_cc: (\forall P:Prop. P) \to \forall x. (S x = O).
-intros. apply H.
-qed.
-
-theorem eq_gen_S_S: \forall m,n. (S m) = (S n) \to m = n. 
-intros. cut ((pred (S m)) = (pred (S n))). 
-assumption. elim H. auto paramodulation.
-qed.
-
-theorem eq_gen_S_S_cc: \forall m,n. m = n \to (S m) = (S n).
-intros. elim H. auto paramodulation.
+theorem eq_S_S: \forall m,n. m = n \to (S m) = (S n).
+intros; destruct; autobatch.
 qed.
 
 inductive le: nat \to nat \to Prop \def
@@ -63,53 +24,57 @@ inductive le: nat \to nat \to Prop \def
    | le_succ: \forall m, n. (le m n) \to (le (S m) (S n)).
 
 theorem le_refl: \forall x. (le x x).
-intros. elim x; auto new.
+intros; elim x; clear x; autobatch.
 qed.
 
-theorem le_gen_x_O_aux: \forall x, y. (le x y) \to (y =O) \to 
-                        (x = O).
-intros 3. elim H. auto paramodulation. apply eq_gen_S_O. exact n1. auto paramodulation.
+theorem le_gen_x_O_aux: \forall x, y. (le x y) \to (y =O) \to (x = O).
+intros 3; elim H; clear H x y;
+[ autobatch
+| destruct
+]
 qed.
 
 theorem le_gen_x_O: \forall x. (le x O) \to (x = O).
-intros. apply le_gen_x_O_aux. exact O. auto paramodulation. auto paramodulation.
+intros; lapply linear le_gen_x_O_aux to H;
+[ destruct; autobatch
+| autobatch
+].
 qed.
 
-theorem le_gen_x_O_cc: \forall x. (x = O) \to (le x O).
-intros. elim H. auto new.
+theorem le_x_O: \forall x. (x = O) \to (le x O).
+intros; destruct; autobatch.
 qed.
 
 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 paramodulation.
-cut (n = m). elim Hcut. apply ex_intro. exact n1. auto new.auto paramodulation.
+intros 4; elim H; clear H x y;
+[ destruct
+| destruct; autobatch
+].
 qed.
 
 theorem le_gen_S_x: \forall m,x. (le (S m) x) \to 
                     (\exists n. x = (S n) \land (le m n)).
-intros. apply le_gen_S_x_aux. exact (S m). auto paramodulation. auto paramodulation.
+intros; lapply le_gen_S_x_aux to H; autobatch.
 qed.
 
-theorem le_gen_S_x_cc: \forall m,x. (\exists n. x = (S n) \land (le m n)) \to
-                       (le (S m) x).
-intros. elim H. elim H1. cut ((S x1) = x). elim Hcut. auto new.
-elim H2. auto paramodulation.
+theorem le_S_x: \forall m,x. (\exists n. x = (S n) \land (le m n)) \to
+                (le (S m) x).
+intros; decompose; destruct; autobatch.
 qed.
 
 theorem le_gen_S_S: \forall m,n. (le (S m) (S n)) \to (le m n).
 intros.
-lapply le_gen_S_x to H as H0. elim H0. elim H1. 
-lapply eq_gen_S_S to H2 as H4. rewrite > H4. assumption.
+lapply linear le_gen_S_x to H as H0; decompose; destruct; autobatch.
 qed.
 
-theorem le_gen_S_S_cc: \forall m,n. (le m n) \to (le (S m) (S n)).
-intros. auto new.
+theorem le_S_S: \forall m,n. (le m n) \to (le (S m) (S n)).
+intros; autobatch.
 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 paramodulation.
-fwd H1 [H]. decompose H.
-*)
+intros 3. elim H; clear H x y;
+[ autobatch
+| lapply linear le_gen_S_x to H3; decompose; destruct; autobatch.
+].
+qed.