set "baseuri" "cic:/matita/LAMBDA-TYPES/Level-1/Base/ext/preamble".
-(* FG: We should include legacy/coq.ma bit it is not working *)
-(* include "legacy/coq.ma". *)
+include "legacy/coq.ma".
-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.
-
-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 plus" 'plus x y = (cic:/Coq/Init/Peano/plus.con x y).
-interpretation "Coq's natural 'less or equal to'" 'leq x y = (cic:/Coq/Init/Peano/le.ind#xpointer(1/1) x y).
-
-alias id "land" = "cic:/Coq/Init/Logic/and.ind#xpointer(1/1)".
-
(* FG/CSC: These aliases should disappear: we would like to write something
* like: "disambiguate in cic:/Coq/*"
*)
alias id "lt_le_trans" = "cic:/Coq/Arith/Lt/lt_le_trans.con".
alias id "lt_wf_ind" = "cic:/Coq/Arith/Wf_nat/lt_wf_ind.con".
alias id "bool_ind" = "cic:/Coq/Init/Datatypes/bool_ind.con".
+alias id "ex_ind" = "cic:/Coq/Init/Logic/ex_ind.con".
+alias id "plus_Snm_nSm" = "cic:/Coq/Arith/Plus/plus_Snm_nSm.con".
+alias id "plus_lt_le_compat" = "cic:/Coq/Arith/Plus/plus_lt_le_compat.con".
+alias id "plus_lt_compat" = "cic:/Coq/Arith/Plus/plus_lt_compat.con".
theorem f_equal: \forall A,B:Type. \forall f:A \to B.
\forall x,y:A. x = y \to f x = f y.
qed.
definition sym_equal \def sym_eq.
+
+default "equality"
+ cic:/Coq/Init/Logic/eq.ind
+ cic:/matita/LAMBDA-TYPES/Level-1/Base/ext/preamble/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:/matita/LAMBDA-TYPES/Level-1/Base/ext/preamble/f_equal.con
+ cic:/matita/legacy/coq/f_equal1.con.