Commit db02ca8d by Samuel Ben Hamou

### Petits détails, correction des axiomes.

parent 934da1dd
 ... ... @@ -311,6 +311,8 @@ Grâce à ce résultat, la preuve d'un théorème $\phi$ utilisant des lemmes au \subsection{Encodage des axiomes et méta-théorèmes} % achtung parsing \subsection{Preuves exemples} \subsection{Construction de $\N$} ... ...
 ... ... @@ -84,11 +84,11 @@ Definition eq_trans := ∀∀∀ (#2 = #1 /\ #1 = #0 -> #2 = #0). Definition compat_left := ∀∀∀ (#0 = #1 /\ #0 ∈ #2 -> #1 ∈ #2). Definition compat_right := ∀∀∀ (#0 ∈ #1 /\ #1 = #2 -> #0 ∈ #2). Definition ext := ∀∀ (∀ (#0 ∈ #2 <-> #0 ∈ #1) -> #2 = #1). Definition ext := ∀∀ ((∀ #0 ∈ #2 <-> #0 ∈ #1) -> #1 = #0). Definition pairing := ∀∀∃∀ (#0 ∈ #1 <-> #0 = #3 \/ #0 = #2). Definition union := ∀∃∀ (#0 ∈ #1 <-> ∃ (#0 ∈ #3 /\ #1 ∈ #0)). Definition powerset := ∀∃∀ (#0 ∈ #1 <-> ∀ (#0 ∈ #1 -> #0 ∈ #3)). Definition infinity := ∃ (∃ (#0 ∈ #1 /\ zero (#0)) /\ ∀ (#0 ∈ #1 -> (∃ (#0 ∈ #2 /\ succ (#1) (#0))))). Definition infinity := ∃ (∃ ((#0 ∈ #1 /\ zero (#0)) /\ ∀ (#0 ∈ #1 -> (∃ (#0 ∈ #2 /\ succ (#1) (#0)))))). Definition axioms_list := [ eq_refl; eq_sym; eq_trans; compat_left; compat_right; ext; pairing; union; powerset; infinity ]. ... ... @@ -127,7 +127,7 @@ Definition replacement_schema A := nForall ((level A) - 3) (∀ (∀ (#0 ∈ #1 -> exists_uniq A)) -> ∃∀ (#0 ∈ #2 -> ∃ (#0 ∈ #3 /\ lift_form_above 2 A))). ∃∀ (#0 ∈ #2 -> ∃ (#0 ∈ #2 /\ lift_form_above 2 A))). Local Close Scope formula_scope. ... ...
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