refactoring of \lambda\delta version 1 in matita

[helm.git] / matitaB / matita / contribs / LAMBDA-TYPES / Legacy-1 / coq / defs.ma

diff --git a/matitaB/matita/contribs/LAMBDA-TYPES/Legacy-1/coq/defs.ma b/matitaB/matita/contribs/LAMBDA-TYPES/Legacy-1/coq/defs.ma
deleted file mode 100644 (file)
index 7d46962..0000000
--- a/matitaB/matita/contribs/LAMBDA-TYPES/Legacy-1/coq/defs.ma
+++ /dev/null
@@ -1,99 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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-1/preamble.ma".
-
-inductive eq (A: Set) (x: A): A \to Prop \def
-| refl_equal: eq A x x.
-
-inductive True: Prop \def
-| I: True.
-
-inductive land (A: Prop) (B: Prop): Prop \def
-| conj: A \to (B \to (land A B)).
-
-inductive or (A: Prop) (B: Prop): Prop \def
-| or_introl: A \to (or A B)
-| or_intror: B \to (or A B).
-
-inductive ex (A: Set) (P: A \to Prop): Prop \def
-| ex_intro: \forall (x: A).((P x) \to (ex A P)).
-
-inductive ex2 (A: Set) (P: A \to Prop) (Q: A \to Prop): Prop \def
-| ex_intro2: \forall (x: A).((P x) \to ((Q x) \to (ex2 A P Q))).
-
-definition not:
- Prop \to Prop
-\def
- \lambda (A: Prop).(A \to False).
-
-inductive bool: Set \def
-| true: bool
-| false: bool.
-
-inductive nat: Set \def
-| O: nat
-| S: nat \to nat.
-
-inductive le (n: nat): nat \to Prop \def
-| le_n: le n n
-| le_S: \forall (m: nat).((le n m) \to (le n (S m))).
-
-definition lt:
- nat \to (nat \to Prop)
-\def
- \lambda (n: nat).(\lambda (m: nat).(le (S n) m)).
-
-definition IsSucc:
- nat \to Prop
-\def
- \lambda (n: nat).(match n with [O \Rightarrow False | (S _) \Rightarrow 
-True]).
-
-definition pred:
- nat \to nat
-\def
- \lambda (n: nat).(match n with [O \Rightarrow O | (S u) \Rightarrow u]).
-
-definition plus:
- nat \to (nat \to nat)
-\def
- let rec plus (n: nat) on n: (nat \to nat) \def (\lambda (m: nat).(match n 
-with [O \Rightarrow m | (S p) \Rightarrow (S (plus p m))])) in plus.
-
-definition minus:
- nat \to (nat \to nat)
-\def
- let rec minus (n: nat) on n: (nat \to nat) \def (\lambda (m: nat).(match n 
-with [O \Rightarrow O | (S k) \Rightarrow (match m with [O \Rightarrow (S k) 
-| (S l) \Rightarrow (minus k l)])])) in minus.
-
-inductive Acc (A: Set) (R: A \to (A \to Prop)): A \to Prop \def
-| Acc_intro: \forall (x: A).(((\forall (y: A).((R y x) \to (Acc A R y)))) \to 
-(Acc A R x)).
-
-definition well_founded:
- \forall (A: Set).(((A \to (A \to Prop))) \to Prop)
-\def
- \lambda (A: Set).(\lambda (R: ((A \to (A \to Prop)))).(\forall (a: A).(Acc A 
-R a))).
-
-definition ltof:
- \forall (A: Set).(((A \to nat)) \to (A \to (A \to Prop)))
-\def
- \lambda (A: Set).(\lambda (f: ((A \to nat))).(\lambda (a: A).(\lambda (b: 
-A).(lt (f a) (f b))))).
-