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Commit f6664df5 authored by Robbert Krebbers's avatar Robbert Krebbers
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Left and right mononicity properties for uPred_and and uPred_or.

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......@@ -436,8 +436,16 @@ Lemma const_mono φ1 φ2 : (φ1 → φ2) → ■ φ1 ⊑ ■ φ2.
Proof. intros; apply const_elim with φ1; eauto using const_intro. 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').
Proof. by intros; apply and_mono. Qed.
Lemma and_mono_r P P' Q' : P' ⊑ Q' → (P ∧ P') ⊑ (P ∧ Q').
Proof. by apply and_mono. Qed.
Lemma or_mono P P' Q Q' : P ⊑ Q → P' ⊑ Q' → (P ∨ P') ⊑ (Q ∨ Q').
Proof. auto. Qed.
Lemma or_mono_l P P' Q : P ⊑ Q → (P ∨ P') ⊑ (Q ∨ P').
Proof. by intros; apply or_mono. Qed.
Lemma or_mono_r P P' Q' : P' ⊑ Q' → (P ∨ P') ⊑ (P ∨ Q').
Proof. by apply or_mono. Qed.
Lemma impl_mono P P' Q Q' : Q ⊑ P → P' ⊑ Q' → (P → P') ⊑ (Q → Q').
Proof.
intros HP HQ'; apply impl_intro_l; rewrite -HQ'.
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