Commit 406637f4 authored by Robbert Krebbers's avatar Robbert Krebbers

Prove later_intro in the logic; it follows from Löb.

parent 35b80fee
......@@ -1009,11 +1009,6 @@ Lemma later_mono P Q : (P ⊢ Q) → ▷ P ⊢ ▷ Q.
Proof.
unseal=> HP; split=>-[|n] x ??; [done|apply HP; eauto using cmra_validN_S].
Qed.
Lemma later_intro P : P P.
Proof.
unseal; split=> -[|n] x ??; simpl in *; [done|].
apply uPred_closed with (S n); eauto using cmra_validN_S.
Qed.
Lemma löb P : ( P P) P.
Proof.
unseal; split=> n x ? HP; induction n as [|n IH]; [by apply HP|].
......@@ -1049,6 +1044,12 @@ Proof. intros P Q; apply later_mono. Qed.
Global Instance later_flip_mono' :
Proper (flip () ==> flip ()) (@uPred_later M).
Proof. intros P Q; apply later_mono. Qed.
Lemma later_intro P : P P.
Proof.
rewrite -(and_elim_l ( P) P) -(löb ( P P)) later_and.
apply impl_intro_l; auto.
Qed.
Lemma later_True : True True.
Proof. apply (anti_symm ()); auto using later_intro. Qed.
Lemma later_impl P Q : (P Q) P Q.
......
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