added definition of f_equal1. I think this file should not be inside the matita library!

[helm.git] / matita / library / legacy / coq.ma

diff --git a/matita/library/legacy/coq.ma b/matita/library/legacy/coq.ma
index d3c74fe21e88a02b6ab4e502fcf79c669af0bc19..8669d1ef7e0715cbe602ea0465df1701a01bed03 100644 (file)
--- a/matita/library/legacy/coq.ma
+++ b/matita/library/legacy/coq.ma
@@ -14,6 +14,22 @@
 
 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).
@@ -56,3 +72,13 @@ interpretation "Coq's real 'greater than'" 'gt x y = (cic:/Coq/Reals/Rdefinition
 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.
+