set "baseuri" "cic:/matita/legacy/coq/".
+default "equality"
+ cic:/Coq/Init/Logic/eq.ind
+ cic:/Coq/Init/Logic/sym_eq.con
+ cic:/Coq/Init/Logic/trans_eq.con
+ cic:/Coq/Init/Logic/eq_ind.con
+ cic:/Coq/Init/Logic/eq_ind_r.con
+ cic:/Coq/Init/Logic/f_equal.con
+ cic:/Coq/Init/Logic/f_equal1.con.
+
+default "true"
+ cic:/Coq/Init/Logic/True.ind.
+default "false"
+ cic:/Coq/Init/Logic/False.ind.
+default "absurd"
+ cic:/Coq/Init/Logic/absurd.con.
+
(* aritmetic operators *)
interpretation "Coq's natural plus" 'plus x y = (cic:/Coq/Init/Peano/plus.con x y).
interpretation "Coq's leibnitz's equality" 'eq x y = (cic:/Coq/Init/Logic/eq.ind#xpointer(1/1) _ x y).
interpretation "Coq's not equal to (leibnitz)" 'neq x y = (cic:/Coq/Init/Logic/not.con (cic:/Coq/Init/Logic/eq.ind#xpointer(1/1) _ x y)).
+interpretation "Coq's natural 'not less or equal than'"
+ 'nleq x y = (cic:/Coq/Init/Logic/not.con
+ (cic:/Coq/Init/Peano/le.ind#xpointer(1/1) x y)).
+
+theorem f_equal1 :
+ \forall A,B:Type. \forall f:A \to B. \forall x,y:A.
+ x = y \to f y = f x.
+ intros.elim H.reflexivity.
+qed.
+