Commit 175ae7e6 authored by Robbert Krebbers's avatar Robbert Krebbers
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Prove (P ≡ Q) ⊢ (P Q).

parent 5e384379
......@@ -683,6 +683,7 @@ Lemma const_elim_r φ Q R : (φ → Q ⊢ R) → (Q ∧ ■ φ) ⊢ R.
Proof. intros; apply const_elim with φ; eauto. Qed.
Lemma const_equiv (φ : Prop) : φ ( φ) ⊣⊢ True.
Proof. intros; apply (anti_symm _); auto using const_intro. Qed.
Lemma eq_refl' {A : cofeT} (a : A) P : P (a a).
Proof. rewrite (True_intro P). apply eq_refl. Qed.
Hint Resolve eq_refl'.
......@@ -690,6 +691,10 @@ Lemma equiv_eq {A : cofeT} P (a b : A) : a ≡ b → P ⊢ (a ≡ b).
Proof. by intros ->. Qed.
Lemma eq_sym {A : cofeT} (a b : A) : (a b) (b a).
Proof. apply (eq_rewrite a b (λ b, b a)%I); auto. solve_proper. Qed.
Lemma eq_iff P Q : (P Q) (P Q).
apply (eq_rewrite P Q (λ Q, P Q))%I; first solve_proper; auto using iff_refl.
(* BI connectives *)
Lemma sep_mono P P' Q Q' : P Q P' Q' (P P') (Q Q').
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