Commit 31a4ea00 by Samuel Ben Hamou

### Début preuve WfAx.

parent 2e0ef968
 ... ... @@ -12,7 +12,7 @@ Local Open Scope eqb_scope. (* The naive set theory consists of the non restricted comprehension axiom schema : ∀ x1, ..., ∀ xn, ∃ a, ∀ y (y ∈ a <-> A), forall formula A whose free variable are amongst x1, ..., xn, y. *) forall formula A whose free variables are amongst x1, ..., xn, y. *) Notation "x ∈ y" := (Pred "∈" [x;y]) (at level 70) : formula_scope. ... ... @@ -101,7 +101,7 @@ Definition IsAx A := List.In A axioms_list \/ (exists B, A = separation_schema B /\ check ZFSign B = true /\ FClosed B). FClosed B) \/ (exists B, A = replacement_schema B /\ check ZFSign B = true /\ ... ... @@ -109,14 +109,17 @@ Definition IsAx A := Lemma WfAx A : IsAx A -> Wf ZFSign A. Proof. intros [ IN | (B & -> & HB & HB') ]. intros [ IN | [ (B & -> & HB & HB') | (C & -> & HC & HC') ] ]. - apply Wf_iff. unfold axioms_list in IN. simpl in IN. intuition; subst; reflexivity. - repeat split; unfold separation_schema; cbn. + rewrite nForall_check. cbn. rewrite !check_bsubst, HB; auto. + red. rewrite nForall_level. cbn. apply andb_true_iff. split. * assumption. * apply orb_true_iff. left. assumption. + red. rewrite nForall_level. SearchAbout level. assert (level (bsubst 0 Zero B) <= level B). { apply level_bsubst'. auto. } assert (level (bsubst 0 (Succ(BVar 0)) B) <= level B). ... ...
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