Commit 575f23a9 authored by Ralf Jung's avatar Ralf Jung

rename _setoid suffix to _equiv; add variant of fmap_Some_setoid that can be usefully destructed

parent a4fe5037
......@@ -556,7 +556,7 @@ Proof. apply map_eq; intros i; by rewrite lookup_fmap, option_fmap_id. Qed.
Lemma map_fmap_compose {A B C} (f : A B) (g : B C) (m : M A) :
g f <$> m = g <$> f <$> m.
Proof. apply map_eq; intros i; by rewrite !lookup_fmap,option_fmap_compose. Qed.
Lemma map_fmap_setoid_ext `{Equiv A, Equiv B} (f1 f2 : A B) m :
Lemma map_fmap_equiv_ext `{Equiv A, Equiv B} (f1 f2 : A B) m :
( i x, m !! i = Some x f1 x f2 x) f1 <$> m f2 <$> m.
Proof.
intros Hi i; rewrite !lookup_fmap.
......
......@@ -2802,7 +2802,7 @@ Section fmap.
Lemma list_fmap_ext (g : A B) (l1 l2 : list A) :
( x, f x = g x) l1 = l2 fmap f l1 = fmap g l2.
Proof. intros ? <-. induction l1; f_equal/=; auto. Qed.
Lemma list_fmap_setoid_ext `{Equiv B} (g : A B) l :
Lemma list_fmap_equiv_ext `{Equiv B} (g : A B) l :
( x, f x g x) f <$> l g <$> l.
Proof. induction l; constructor; auto. Qed.
......
......@@ -180,7 +180,7 @@ Proof. unfold is_Some; destruct mx; naive_solver. Qed.
Lemma fmap_Some {A B} (f : A B) mx y :
f <$> mx = Some y x, mx = Some x y = f x.
Proof. destruct mx; naive_solver. Qed.
Lemma fmap_Some_setoid {A B} `{Equiv B} `{!Equivalence (() : relation B)}
Lemma fmap_Some_equiv {A B} `{Equiv B} `{!Equivalence (() : relation B)}
(f : A B) mx y :
f <$> mx Some y x, mx = Some x y f x.
Proof.
......@@ -190,6 +190,10 @@ Proof.
- intros ?%symmetry%equiv_None. done.
- intros (? & ? & ?). done.
Qed.
Lemma fmap_Some_equiv' {A B} `{Equiv B} `{!Equivalence (() : relation B)}
(f : A B) mx y :
f <$> mx Some y x, mx = Some x y f x.
Proof. intros. apply fmap_Some_equiv. done. Qed.
Lemma fmap_None {A B} (f : A B) mx : f <$> mx = None mx = None.
Proof. by destruct mx. Qed.
Lemma option_fmap_id {A} (mx : option A) : id <$> mx = mx.
......@@ -200,7 +204,7 @@ Proof. by destruct mx. Qed.
Lemma option_fmap_ext {A B} (f g : A B) mx :
( x, f x = g x) f <$> mx = g <$> mx.
Proof. intros; destruct mx; f_equal/=; auto. Qed.
Lemma option_fmap_setoid_ext `{Equiv A, Equiv B} (f g : A B) mx :
Lemma option_fmap_equiv_ext `{Equiv A, Equiv B} (f g : A B) mx :
( x, f x g x) f <$> mx g <$> mx.
Proof. destruct mx; constructor; auto. Qed.
Lemma option_fmap_bind {A B C} (f : A B) (g : B option C) mx :
......
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment