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[helm.git] / matita / contribs / LAMBDA-TYPES / Legacy-2 / preamble.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "Legacy-1/definitions.ma".
+
+default "equality"
+ cic:/matita/LAMBDA-TYPES/Legacy-1/coq/defs/eq.ind
+ cic:/matita/LAMBDA-TYPES/Legacy-1/coq/props/sym_eq.con
+ cic:/matita/LAMBDA-TYPES/Legacy-1/coq/props/trans_eq.con
+ cic:/matita/LAMBDA-TYPES/Legacy-1/coq/defs/eq_ind.con
+ cic:/matita/LAMBDA-TYPES/Legacy-1/coq/props/eq_ind_r.con
+ cic:/matita/LAMBDA-TYPES/Legacy-1/coq/defs/eq_rec.con
+ cic:/matita/LAMBDA-TYPES/Legacy-1/coq/props/eq_rec_r.con
+ cic:/matita/LAMBDA-TYPES/Legacy-1/coq/defs/eq_rect.con
+ cic:/matita/LAMBDA-TYPES/Legacy-1/coq/props/eq_rect_r.con
+ cic:/matita/LAMBDA-TYPES/Legacy-1/coq/props/f_equal.con
+ cic:/matita/LAMBDA-TYPES/Legacy-2/preamble/f_equal_sym.con.
+
+default "true"
+ cic:/matita/LAMBDA-TYPES/Legacy-1/coq/defs/True.ind. 
+default "false"
+ cic:/matita/LAMBDA-TYPES/Legacy-1/preamble/False.ind. 
+default "absurd"
+ cic:/matita/LAMBDA-TYPES/Legacy-1/coq/props/absurd.con. 
+
+interpretation "Coq 7.3.1 natural plus" 'plus x y = (cic:/matita/LAMBDA-TYPES/Legacy-1/coq/defs/plus.con x y).
+interpretation "Coq 7.3.1 natural minus" 'minus x y = (cic:/matita/LAMBDA-TYPES/Legacy-1/coq/defs/minus.con x y).
+interpretation "Coq 7.3.1 logical and" 'and x y = (cic:/matita/LAMBDA-TYPES/Legacy-1/coq/defs/land.ind#xpointer(1/1) x y).
+interpretation "Coq 7.3.1 logical or" 'or x y = (cic:/matita/LAMBDA-TYPES/Legacy-1/coq/defs/or.ind#xpointer(1/1) x y).
+interpretation "Coq 7.3.1 logical not" 'not x = (cic:/matita/LAMBDA-TYPES/Legacy-1/coq/defs/not.con x).
+interpretation "Coq 7.3.1 exists" 'exists \eta.x = (cic:/matita/LAMBDA-TYPES/Legacy-1/coq/defs/ex.ind#xpointer(1/1) _ x).
+interpretation "Coq 7.3.1 natural 'less or equal to'" 'leq x y = (cic:/matita/LAMBDA-TYPES/Legacy-1/coq/defs/le.ind#xpointer(1/1) x y).
+interpretation "Coq 7.3.1 natural 'less than'" 'lt x y = (cic:/matita/LAMBDA-TYPES/Legacy-1/coq/defs/lt.con x y).
+interpretation "Coq 7.3.1 leibnitz's equality" 'eq x y = (cic:/matita/LAMBDA-TYPES/Legacy-1/coq/defs/eq.ind#xpointer(1/1) _ x y).
+
+alias symbol "plus" = "Coq 7.3.1 natural plus".
+alias symbol "minus" = "Coq 7.3.1 natural minus".
+alias symbol "and" = "Coq 7.3.1 logical and".
+alias symbol "or" = "Coq 7.3.1 logical or".
+alias symbol "not" = "Coq 7.3.1 logical not".
+alias symbol "exists" = "Coq 7.3.1 exists".
+alias symbol "leq" = "Coq 7.3.1 natural 'less or equal to'".
+alias symbol "lt" = "Coq 7.3.1 natural 'less than'".
+alias symbol "eq" = "Coq 7.3.1 leibnitz's equality".
+
+theorem f_equal_sym: \forall A,B:Set.\forall f:A\to B.\forall x,y.
+                     x = y \to (f y) = (f x).
+  intros; symmetry.
+  apply cic:/matita/LAMBDA-TYPES/Legacy-1/coq/props/f_equal.con.
+  assumption.
+qed.