Commit a530466b authored by Samuel Ben Hamou's avatar Samuel Ben Hamou
Browse files

Recorrection des dépendances circulaires (mauvais revert...)

parent c9783d14
......@@ -279,8 +279,15 @@ Proof.
apply R_All_e with (t := Succ (FVar "y")) in AX10; auto.
Qed.
Lemma Comm : IsTheorem Intuiti PeanoTheory (∀∀ (#0 + #1 = #1 + #0)).
Admitted.
Lemma Comm :
IsTheorem Intuiti PeanoTheory
( (#0 = #0 + Zero) -> ∀∀ (Succ(#1 + #0) = #1 + Succ(#0)) ->
∀∀ (#0 + #1 = #1 + #0)).
Proof.
assert (IsTheorem Intuiti PeanoTheory ( (#0 = #0 + Zero)) -> IsTheorem Intuiti PeanoTheory (∀∀ (Succ(#1 + #0) = #1 + Succ(#0)) -> ∀∀ (#0 + #1 = #1 + #0)) -> IsTheorem Intuiti PeanoTheory ( (#0 = #0 + Zero) -> ∀∀ (Succ(#1 + #0) = #1 + Succ(#0)) -> ∀∀ (#0 + #1 = #1 + #0))).
{ apply ModusPonens. }
apply ModusPonens with (A := (#0 = #0 + Zero)).
(** A Coq model of this Peano theory, based on the [nat] type *)
......
......@@ -4,7 +4,7 @@
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Defs NameProofs Mix Meta Countable Models.
Require Import Defs NameProofs Mix Meta Countable.
Import ListNotations.
Local Open Scope bool_scope.
Local Open Scope eqb_scope.
......
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