Commit 9312ad02 authored by Paolo G. Giarrusso's avatar Paolo G. Giarrusso

Clearer statement for propositional extensionality

- And use prop_ext instead of prop_ext_2 in other proofs.
parent 69971a15
......@@ -159,6 +159,8 @@ Changes in Coq:
fractional camera (`frac_auth`) with unbounded fractions.
* Changed `frac_auth` notation from `●!`/`◯!` to `●F`/`◯F`. sed script:
`s/◯!/◯F/g; s/●!/●F/g;`.
* Lemma `prop_ext` works in both directions; its default direction is the
opposite of what it used to be.
* Rename `C` suffixes into `O` since we no longer use COFEs but OFEs. Also
rename `ofe_fun` into `discrete_fun` and the corresponding notation `-c>` into
`-d>`. The renaming can be automatically done using the following script (on
......
......@@ -923,7 +923,7 @@ Proof.
- intros P. split=> i /=. apply bi.forall_intro=>_. by apply plainly_emp_intro.
- intros P Q. split=> i. apply bi.sep_elim_l, _.
- intros P Q. split=> i /=. rewrite (monPred_equivI P Q). f_equiv=> j.
by rewrite -prop_ext_2 !(bi.forall_elim j) !bi.pure_True // !bi.True_impl.
by rewrite prop_ext !(bi.forall_elim j) !bi.pure_True // !bi.True_impl.
- intros P. split=> i /=.
rewrite bi.later_forall. f_equiv=> j. by rewrite -later_plainly_1.
- intros P. split=> i /=.
......
......@@ -467,10 +467,19 @@ Proof.
rewrite -(internal_eq_refl True%I a) plainly_pure; auto.
Qed.
Lemma prop_ext P Q : P Q ⊣⊢ (P - Q).
Proof.
apply (anti_symm ()); last exact: prop_ext_2.
apply (internal_eq_rewrite' P Q (λ Q, (P - Q))%I);
[ solve_proper | done | ].
rewrite (plainly_emp_intro (P Q)%I).
apply plainly_mono, wand_iff_refl.
Qed.
Lemma plainly_alt P : P ⊣⊢ <affine> P emp.
Proof.
rewrite -plainly_affinely_elim. apply (anti_symm ()).
- rewrite -prop_ext_2. apply plainly_mono, and_intro; apply wand_intro_l.
- rewrite prop_ext. apply plainly_mono, and_intro; apply wand_intro_l.
+ by rewrite affinely_elim_emp left_id.
+ by rewrite left_id.
- rewrite internal_eq_sym (internal_eq_rewrite _ _ plainly).
......@@ -480,7 +489,7 @@ Qed.
Lemma plainly_alt_absorbing P `{!Absorbing P} : P ⊣⊢ P True.
Proof.
apply (anti_symm ()).
- rewrite -prop_ext_2. apply plainly_mono, and_intro; apply wand_intro_l; auto.
- rewrite prop_ext. apply plainly_mono, and_intro; apply wand_intro_l; auto.
- rewrite internal_eq_sym (internal_eq_rewrite _ _ plainly).
by rewrite plainly_pure True_impl.
Qed.
......@@ -488,7 +497,7 @@ Qed.
Lemma plainly_True_alt P : (True - P) ⊣⊢ P True.
Proof.
apply (anti_symm ()).
- rewrite -prop_ext_2. apply plainly_mono, and_intro; apply wand_intro_l; auto.
- rewrite prop_ext. apply plainly_mono, and_intro; apply wand_intro_l; auto.
by rewrite wand_elim_r.
- rewrite internal_eq_sym (internal_eq_rewrite _ _
(λ Q, (True - Q))%I ltac:(shelve)); last solve_proper.
......
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