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Commit 824257bc authored by Robbert Krebbers's avatar Robbert Krebbers
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Anti symmetry for sets.

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...@@ -24,6 +24,8 @@ Section simple_collection. ...@@ -24,6 +24,8 @@ Section simple_collection.
Proof. firstorder auto. Qed. Proof. firstorder auto. Qed.
Global Instance: JoinSemiLattice C. Global Instance: JoinSemiLattice C.
Proof. firstorder auto. Qed. Proof. firstorder auto. Qed.
Global Instance: AntiSymm (≡) (@collection_subseteq A C _).
Proof. done. Qed.
Lemma elem_of_subseteq X Y : X ⊆ Y ↔ ∀ x, x ∈ X → x ∈ Y. Lemma elem_of_subseteq X Y : X ⊆ Y ↔ ∀ x, x ∈ X → x ∈ Y.
Proof. done. Qed. Proof. done. Qed.
Lemma elem_of_equiv X Y : X ≡ Y ↔ ∀ x, x ∈ X ↔ x ∈ Y. Lemma elem_of_equiv X Y : X ≡ Y ↔ ∀ x, x ∈ X ↔ x ∈ Y.
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