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Fix fixpoint import error and ExclBot -> ExclInvalid rename #16

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Fix fixpoint import error and ExclBot -> ExclInvalid rename #16

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2 changes: 1 addition & 1 deletion theories/gr_predicates.v
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Original file line number Diff line number Diff line change
@@ -1,4 +1,4 @@
From iris.bi Require Export fixpoint.
From iris.bi Require Export fixpoint_mono.
From iris.heap_lang Require Import lang proofmode notation.

(* ################################################################# *)
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16 changes: 8 additions & 8 deletions theories/resource_algebra.v
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Original file line number Diff line number Diff line change
Expand Up @@ -604,7 +604,7 @@ Context {A : ofe}.
(**
The carrier of the exclusive RA, [excl], is the same as the carrier of
the underlying resource algebra with the addition of a bottom element,
denoted [ExclBot].
denoted [ExclInvalid].
*)

Print excl.
Expand All @@ -617,33 +617,33 @@ Lemma excl_core (ea : excl A) : pcore ea ≡ None.
Proof. constructor. Qed.

(**
Crucially, all elements except [ExclBot] are valid.
Crucially, all elements except [ExclInvalid] are valid.
*)

Lemma excl_valid (a : A) : ✓ (Excl a).
Proof. constructor. Qed.

Lemma excl_bot_invalid : ¬ (✓ (ExclBot : excl A)).
Lemma excl_bot_invalid : ¬ (✓ (ExclInvalid : excl A)).
Proof.
intros contra.
inversion contra.
Qed.

(**
And the combination of any two elements gives the invalid [ExclBot].
And the combination of any two elements gives the invalid [ExclInvalid].
*)

Lemma excl_op (ea eb : excl A) : ea ⋅ eb ≡ ExclBot.
Lemma excl_op (ea eb : excl A) : ea ⋅ eb ≡ ExclInvalid.
Proof. constructor. Qed.

(**
Let us return to our beloved dfrac. While the operation for dfrac adds
two dfrac fractions together, the operation for two _exclusive_ dfrac
fractions simply results in [ExclBot].
fractions simply results in [ExclInvalid].
*)

Example excl_op_dfrac :
(Excl (DfracOwn (1/4))) ⋅ (Excl (DfracOwn (2/4))) ≡ ExclBot.
(Excl (DfracOwn (1/4))) ⋅ (Excl (DfracOwn (2/4))) ≡ ExclInvalid.
Proof. constructor. Qed.

End exclusive.
Expand All @@ -668,7 +668,7 @@ Lemma token_valid : ✓ tok.
Proof. apply excl_valid. Qed.

(** ... but having the token twice gives the bottom element... *)
Lemma token_token_bot : tok ⋅ tok ≡ ExclBot.
Lemma token_token_bot : tok ⋅ tok ≡ ExclInvalid.
Proof. apply excl_op. Qed.

(* ... which is invalid. *)
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