update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / legacy_1A / coq / fwd.ma

diff --git a/matita/matita/contribs/lambdadelta/legacy_1A/coq/fwd.ma b/matita/matita/contribs/lambdadelta/legacy_1A/coq/fwd.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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+include "legacy_1A/coq/defs.ma".
+
+implied lemma False_rect:
+ \forall (P: Type[0]).(False \to P)
+\def
+ \lambda (P: Type[0]).(\lambda (f: False).(match f in False with [])).
+
+implied lemma False_ind:
+ \forall (P: Prop).(False \to P)
+\def
+ \lambda (P: Prop).(False_rect P).
+
+implied lemma land_rect:
+ \forall (A: Prop).(\forall (B: Prop).(\forall (P: Type[0]).(((A \to (B \to 
+P))) \to ((land A B) \to P))))
+\def
+ \lambda (A: Prop).(\lambda (B: Prop).(\lambda (P: Type[0]).(\lambda (f: ((A 
+\to (B \to P)))).(\lambda (a: (land A B)).(match a with [(conj x x0) 
+\Rightarrow (f x x0)]))))).
+
+implied lemma land_ind:
+ \forall (A: Prop).(\forall (B: Prop).(\forall (P: Prop).(((A \to (B \to P))) 
+\to ((land A B) \to P))))
+\def
+ \lambda (A: Prop).(\lambda (B: Prop).(\lambda (P: Prop).(land_rect A B P))).
+
+implied lemma or_ind:
+ \forall (A: Prop).(\forall (B: Prop).(\forall (P: Prop).(((A \to P)) \to 
+(((B \to P)) \to ((or A B) \to P)))))
+\def
+ \lambda (A: Prop).(\lambda (B: Prop).(\lambda (P: Prop).(\lambda (f: ((A \to 
+P))).(\lambda (f0: ((B \to P))).(\lambda (o: (or A B)).(match o with 
+[(or_introl x) \Rightarrow (f x) | (or_intror x) \Rightarrow (f0 x)])))))).
+
+implied lemma ex_ind:
+ \forall (A: Type[0]).(\forall (P: ((A \to Prop))).(\forall (P0: 
+Prop).(((\forall (x: A).((P x) \to P0))) \to ((ex A P) \to P0))))
+\def
+ \lambda (A: Type[0]).(\lambda (P: ((A \to Prop))).(\lambda (P0: 
+Prop).(\lambda (f: ((\forall (x: A).((P x) \to P0)))).(\lambda (e: (ex A 
+P)).(match e with [(ex_intro x x0) \Rightarrow (f x x0)]))))).
+
+implied lemma ex2_ind:
+ \forall (A: Type[0]).(\forall (P: ((A \to Prop))).(\forall (Q: ((A \to 
+Prop))).(\forall (P0: Prop).(((\forall (x: A).((P x) \to ((Q x) \to P0)))) 
+\to ((ex2 A P Q) \to P0)))))
+\def
+ \lambda (A: Type[0]).(\lambda (P: ((A \to Prop))).(\lambda (Q: ((A \to 
+Prop))).(\lambda (P0: Prop).(\lambda (f: ((\forall (x: A).((P x) \to ((Q x) 
+\to P0))))).(\lambda (e: (ex2 A P Q)).(match e with [(ex_intro2 x x0 x1) 
+\Rightarrow (f x x0 x1)])))))).
+
+implied lemma eq_rect:
+ \forall (A: Type[0]).(\forall (x: A).(\forall (P: ((A \to Type[0]))).((P x) 
+\to (\forall (y: A).((eq A x y) \to (P y))))))
+\def
+ \lambda (A: Type[0]).(\lambda (x: A).(\lambda (P: ((A \to 
+Type[0]))).(\lambda (f: (P x)).(\lambda (y: A).(\lambda (e: (eq A x 
+y)).(match e with [refl_equal \Rightarrow f])))))).
+
+implied lemma eq_ind:
+ \forall (A: Type[0]).(\forall (x: A).(\forall (P: ((A \to Prop))).((P x) \to 
+(\forall (y: A).((eq A x y) \to (P y))))))
+\def
+ \lambda (A: Type[0]).(\lambda (x: A).(\lambda (P: ((A \to Prop))).(eq_rect A 
+x P))).
+
+implied rec lemma le_ind (n: nat) (P: (nat \to Prop)) (f: P n) (f0: (\forall 
+(m: nat).((le n m) \to ((P m) \to (P (S m)))))) (n0: nat) (l: le n n0) on l: 
+P n0 \def match l with [le_n \Rightarrow f | (le_S m l0) \Rightarrow (f0 m l0 
+((le_ind n P f f0) m l0))].
+
+implied rec lemma Acc_ind (A: Type[0]) (R: (A \to (A \to Prop))) (P: (A \to 
+Prop)) (f: (\forall (x: A).(((\forall (y: A).((R y x) \to (Acc A R y)))) \to 
+(((\forall (y: A).((R y x) \to (P y)))) \to (P x))))) (a: A) (a0: Acc A R a) 
+on a0: P a \def match a0 with [(Acc_intro x a1) \Rightarrow (f x a1 (\lambda 
+(y: A).(\lambda (r0: (R y x)).((Acc_ind A R P f) y (a1 y r0)))))].
+