- Level-1: added some problems

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

diff --git a/matita/library/legacy/coq.ma b/matita/library/legacy/coq.ma
index 76da7d8984134a87d4fa1bfea5a440e4b688746d..092a11c6ae3e7e38c7c6c083e55dc7a5c554ac56 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).
@@ -60,3 +76,21 @@ 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)).
 
+(* aliases *)
+
+alias id "or" = "cic:/Coq/Init/Logic/or.ind#xpointer(1/1)".
+alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
+alias id "eq" = "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1)".
+alias id "plus" = "cic:/Coq/Init/Peano/plus.con".
+alias id "le_trans" = "cic:/Coq/Arith/Le/le_trans.con".
+alias id "le_plus_r" = "cic:/Coq/Arith/Plus/le_plus_r.con".
+alias id "le" = "cic:/Coq/Init/Peano/le.ind#xpointer(1/1)".
+
+(* theorems *)
+
+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.
+