Commit ae64fb70 authored by Robbert Krebbers's avatar Robbert Krebbers

Put discrete_validI together with the other validIs and shorten its proof.

parent 9bf9afb4
......@@ -833,21 +833,31 @@ Proof. done. Qed.
Lemma valid_weaken {A : cmraT} (a b : A) : (a b) a.
Proof. intros r n _; apply cmra_validN_op_l. Qed.
(* Own and valid derived *)
Lemma ownM_invalid (a : M) : ¬ {0} a uPred_ownM a False.
Proof. by intros; rewrite ownM_valid valid_elim. Qed.
Global Instance ownM_mono : Proper (flip () ==> ()) (@uPred_ownM M).
Proof. move=>a b [c H]. rewrite H ownM_op. eauto. Qed.
(* Products *)
Lemma prod_equivI {A B : cofeT} (x y : A * B) :
(x y)%I (x.1 y.1 x.2 y.2 : uPred M)%I.
Proof. done. Qed.
Lemma prod_validI {A B : cmraT} (x : A * B) :
( x)%I ( x.1 x.2 : uPred M)%I.
Proof. done. Qed.
(* Later *)
Lemma later_equivI {A : cofeT} (x y : later A) :
(x y)%I ( (later_car x later_car y) : uPred M)%I.
Proof. done. Qed.
(* Own and valid derived *)
Lemma ownM_invalid (a : M) : ¬ {0} a uPred_ownM a False.
Proof. by intros; rewrite ownM_valid valid_elim. Qed.
Global Instance ownM_mono : Proper (flip () ==> ()) (@uPred_ownM M).
Proof. move=>a b [c H]. rewrite H ownM_op. eauto. Qed.
(* Discrete *)
(* For equality, there already is timeless_eq *)
Lemma discrete_validI {A : cofeT} `{ x : A, Timeless x}
`{Op A, Valid A, Unit A, Minus A} (ra : RA A) (x : discreteRA ra) :
( x)%I ( x : uPred M)%I.
Proof. done. Qed.
(* Timeless *)
Lemma timelessP_spec P : TimelessP P x n, {n} x P 0 x P n x.
......@@ -962,23 +972,9 @@ Proof. by rewrite -(always_always Q); apply always_entails_r'. Qed.
End uPred_logic.
Section discrete.
Context {A : cofeT} `{ x : A, Timeless x}.
Context {op : Op A} {v : Valid A} `{Unit A, Minus A} (ra : RA A).
(** Internalized properties of discrete RAs *)
(* For equality, there already is timeless_eq *)
Lemma discrete_validI {M} (x : discreteRA ra) :
( x)%I ( x : uPred M)%I.
Proof.
apply (anti_symm ()).
- move=>? n ?. done.
- move=>? n ? ?. by apply: discrete_valid.
Qed.
End discrete.
(* Hint DB for the logic *)
Create HintDb I.
Hint Resolve const_intro.
Hint Resolve or_elim or_intro_l' or_intro_r' : I.
Hint Resolve and_intro and_elim_l' and_elim_r' : I.
Hint Resolve always_mono : I.
......
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