(* *)
(**************************************************************************)
-
-include "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)".
-alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
-alias id "le" = "cic:/matita/tests/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".
+include "logic/connectives.ma".
+include "nat/nat.ma".
definition is_S: nat \to Prop \def
\lambda n. match n with
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. autobatch.
+intros. elim H. elim H1. cut ((S a) = x). elim Hcut. autobatch.
elim H2. autobatch.
qed.