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extensionality

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Dan Frumin 2019-01-22 11:20:15 +01:00
parent ea05bc91fd
commit a27e73014c
1 changed files with 13 additions and 1 deletions
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czf.v
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@ -184,6 +184,12 @@ Proof.
rewrite <- Ha. rewrite <- Hb. apply Hs. rewrite <- Ha. rewrite <- Hb. apply Hs.
Qed. Qed.
Instance subseteq_reflexive : Reflexive (subseteq : relation V).
Proof. intros ?. unfold subseteq, subseteq_V. auto. Qed.
Instance subseteq_transitive : Transitive (subseteq : relation V).
Proof. intros ???. unfold subseteq, subseteq_V. auto. Qed.
Lemma V_ext (a b : V) : Lemma V_ext (a b : V) :
a ⊆ b → b ⊆ a → a ≡ b. a ⊆ b → b ⊆ a → a ≡ b.
Proof. Proof.
@ -200,7 +206,13 @@ Qed.
(** * Axioms *) (** * Axioms *)
(** Extensionality *) (** Extensionality *)
(* ... *) Theorem CZF_extensionality (a b : V) :
a ⊆ b ∧ b ⊆ a ↔ a ≡ b.
Proof.
split.
- intros [? ?]. apply V_ext; auto.
- intros ->. split; auto.
Qed.
(** Paring *) (** Paring *)
Lemma CZF_pairing (x y : V) : Lemma CZF_pairing (x y : V) :