Commit 480bc071 by Robbert Krebbers

Merge branch 'gen_proofmode' of gitlab.mpi-sws.org:FP/iris-coq into gen_proofmode

parents ae01cec5 b61305ae
 ... ... @@ -113,6 +113,16 @@ Lemma True_intro P : P ⊢ True. Proof. by apply pure_intro. Qed. Hint Immediate False_elim. Lemma entails_eq_True P Q : (P ⊢ Q) ↔ ((P → Q)%I ≡ True%I). Proof. split=>EQ. - apply bi.equiv_spec; split; [by apply True_intro|]. apply impl_intro_r. rewrite and_elim_r //. - trans (P ∧ True)%I. + apply and_intro; first done. by apply pure_intro. + rewrite -EQ impl_elim_r. done. Qed. Lemma and_mono P P' Q Q' : (P ⊢ Q) → (P' ⊢ Q') → P ∧ P' ⊢ Q ∧ Q'. Proof. auto. Qed. Lemma and_mono_l P P' Q : (P ⊢ Q) → P ∧ P' ⊢ Q ∧ P'. ... ... @@ -1428,13 +1438,8 @@ Qed. Lemma limit_preserving_entails {A : ofeT} `{Cofe A} (Φ Ψ : A → PROP) : NonExpansive Φ → NonExpansive Ψ → LimitPreserving (λ x, Φ x ⊢ Ψ x). Proof. intros HΦ HΨ c Hc. assert (Heq : ∀ P Q : PROP, (∀ n, (P → Q)%I ≡{n}≡ True%I) ↔ (P -∗ Q)). { intros ??. rewrite -equiv_dist. split=>EQ. - by rewrite -(left_id True%I bi_and P) -EQ impl_elim_l. - apply bi.equiv_spec; split; [by apply True_intro|]. apply impl_intro_l. by rewrite right_id. } apply Heq=>n. rewrite conv_compl. by apply Heq. intros HΦ HΨ c Hc. apply entails_eq_True, equiv_dist=>n. rewrite conv_compl. apply equiv_dist, entails_eq_True. done. Qed. Lemma limit_preserving_equiv {A : ofeT} `{Cofe A} (Φ Ψ : A → PROP) : NonExpansive Φ → NonExpansive Ψ → LimitPreserving (λ x, Φ x ⊣⊢ Ψ x). ... ...
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