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set "baseuri" "cic:/matita/tests/fguidi/".
-include "coq.ma".
+include "legacy/coq.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)".
qed.
theorem eq_gen_S_O_cc: (\forall P:Prop. P) \to \forall x. (S x = O).
-intros. auto. (* paramodulation non trova la prova *)
+intros. auto.
qed.
theorem eq_gen_S_S: \forall m,n. (S m) = (S n) \to m = n.
-intros. cut (pred (S m)) = (pred (S n)).
+intros. cut ((pred (S m)) = (pred (S n))).
assumption. elim H. auto paramodulation.
qed.
(\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 paramodulation. auto. (* paramodulation non trova la prova *)
+cut (n = m). elim Hcut. apply ex_intro. exact n1. auto paramodulation. auto. (* paramodulation non trova la prova *)
qed.
theorem le_gen_S_x: \forall m,x. (le (S m) x) \to
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 paramodulation. elim H2. auto paramodulation.
+intros. elim H. elim H1. cut ((S x1) = x). elim Hcut. auto paramodulation. elim H2. auto paramodulation.
qed.
theorem le_gen_S_S: \forall m,n. (le (S m) (S n)) \to (le m n).