Commit 84cd1f63 authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Document new fupd+plainly laws.

parent c9760db3
......@@ -84,12 +84,21 @@ only make sense for affine logics. From the axioms below, one could derive
[■ P ={E}=∗ P] (see the lemma [fupd_plainly_elim]), which in turn gives
[True ={E}=∗ emp]. *)
Class BiFUpdPlainly (PROP : sbi) `{!BiFUpd PROP, !BiPlainly PROP} := {
(** When proving a fancy update of a plain proposition, you can also prove it
while being allowed to open all invariants. *)
fupd_plainly_mask_empty E (P : PROP) :
(|={E,}=> P) |={E}=> P;
(** A strong eliminator (a la modus ponens) for the wand-fancy-update with a
plain conclusion: We eliminate [R ={E}=∗ ■ P] by supplying an [R], but we get
to keep the [R]. *)
fupd_plainly_keep_l E (P R : PROP) :
(R ={E}= P) R |={E}=> P R;
(** Later "almost" commutes with fancy updates over plain propositions. It
commutes "almost" because of the ◇ modality, which is needed in the definition
of fancy updates so one can remove laters of timeless propositions. *)
fupd_plainly_later E (P : PROP) :
( |={E}=> P) |={E}=> P;
(** Forall quantifiers commute with fancy updates over plain propositions. *)
fupd_plainly_forall_2 E {A} (Φ : A PROP) :
( x, |={E}=> Φ x) |={E}=> x, Φ x
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