Commit 908be24e authored by Robbert Krebbers's avatar Robbert Krebbers

Clean up names in prelude/option.

parent 74960dec
......@@ -64,7 +64,7 @@ Proof.
{ by intros m2; rewrite (symmetry_iff ()) map_equiv_empty; intros ->. }
intros m2 Hm2; rewrite big_opM_insert //.
rewrite (IH (delete i m2)); last by rewrite -Hm2 delete_insert.
destruct (map_equiv_lookup (<[i:=x]> m1) m2 i x)
destruct (map_equiv_lookup_l (<[i:=x]> m1) m2 i x)
as (y&?&Hxy); auto using lookup_insert.
rewrite Hxy -big_opM_insert; last auto using lookup_delete.
by rewrite insert_delete.
......
......@@ -173,11 +173,9 @@ Section setoid.
split; [intros Hm; apply map_eq; intros i|by intros ->].
by rewrite lookup_empty, <-equiv_None, Hm, lookup_empty.
Qed.
Lemma map_equiv_lookup (m1 m2 : M A) i x :
Lemma map_equiv_lookup_l (m1 m2 : M A) i x :
m1 m2 m1 !! i = Some x y, m2 !! i = Some y x y.
Proof.
intros Hm ?. destruct (equiv_Some (m1 !! i) (m2 !! i) x) as (y&?&?); eauto.
Qed.
Proof. generalize (equiv_Some_inv_l (m1 !! i) (m2 !! i) x); naive_solver. Qed.
End setoid.
(** ** General properties *)
......
......@@ -10,69 +10,74 @@ Inductive option_reflect {A} (P : A → Prop) (Q : Prop) : option A → Type :=
(** * General definitions and theorems *)
(** Basic properties about equality. *)
Lemma None_ne_Some {A} (a : A) : None Some a.
Lemma None_ne_Some {A} (x : A) : None Some x.
Proof. congruence. Qed.
Lemma Some_ne_None {A} (a : A) : Some a None.
Lemma Some_ne_None {A} (x : A) : Some x None.
Proof. congruence. Qed.
Lemma eq_None_ne_Some {A} (x : option A) a : x = None x Some a.
Lemma eq_None_ne_Some {A} (mx : option A) x : mx = None mx Some x.
Proof. congruence. Qed.
Instance Some_inj {A} : Inj (=) (=) (@Some A).
Proof. congruence. Qed.
(** The non dependent elimination principle on the option type. *)
Definition default {A B} (b : B) (x : option A) (f : A B) : B :=
match x with None => b | Some a => f a end.
Definition default {A B} (y : B) (mx : option A) (f : A B) : B :=
match mx with None => y | Some x => f x end.
Instance: Params (@default) 2.
(** The [from_option] function allows us to get the value out of the option
type by specifying a default value. *)
Definition from_option {A} (a : A) (x : option A) : A :=
match x with None => a | Some b => b end.
Definition from_option {A} (x : A) (mx : option A) : A :=
match mx with None => x | Some y => y end.
Instance: Params (@from_option) 1.
(** An alternative, but equivalent, definition of equality on the option
data type. This theorem is useful to prove that two options are the same. *)
Lemma option_eq {A} (x y : option A) : x = y a, x = Some a y = Some a.
Proof. split; [by intros; by subst |]. destruct x, y; naive_solver. Qed.
Lemma option_eq_1 {A} (x y : option A) a : x = y x = Some a y = Some a.
Lemma option_eq {A} (mx my: option A): mx = my x, mx = Some x my = Some x.
Proof. split; [by intros; by subst |]. destruct mx, my; naive_solver. Qed.
Lemma option_eq_1 {A} (mx my: option A) x : mx = my mx = Some x my = Some x.
Proof. congruence. Qed.
Lemma option_eq_1_alt {A} (x y : option A) a : x = y y = Some a x = Some a.
Lemma option_eq_1_alt {A} (mx my : option A) x :
mx = my my = Some x mx = Some x.
Proof. congruence. Qed.
Definition is_Some {A} (x : option A) := y, x = Some y.
Lemma mk_is_Some {A} (x : option A) y : x = Some y is_Some x.
Definition is_Some {A} (mx : option A) := x, mx = Some x.
Instance: Params (@is_Some) 1.
Lemma mk_is_Some {A} (mx : option A) x : mx = Some x is_Some mx.
Proof. intros; red; subst; eauto. Qed.
Hint Resolve mk_is_Some.
Lemma is_Some_None {A} : ¬is_Some (@None A).
Proof. by destruct 1. Qed.
Hint Resolve is_Some_None.
Instance is_Some_pi {A} (x : option A) : ProofIrrel (is_Some x).
Instance is_Some_pi {A} (mx : option A) : ProofIrrel (is_Some mx).
Proof.
set (P (y : option A) := match y with Some _ => True | _ => False end).
set (f x := match x return P x is_Some x with
set (P (mx : option A) := match mx with Some _ => True | _ => False end).
set (f mx := match mx return P mx is_Some mx with
Some _ => λ _, ex_intro _ _ eq_refl | None => False_rect _ end).
set (g x (H : is_Some x) :=
match H return P x with ex_intro _ p => eq_rect _ _ I _ (eq_sym p) end).
assert ( x H, f x (g x H) = H) as f_g by (by intros ? [??]; subst).
intros p1 p2. rewrite <-(f_g _ p1), <-(f_g _ p2). by destruct x, p1.
set (g mx (H : is_Some mx) :=
match H return P mx with ex_intro _ p => eq_rect _ _ I _ (eq_sym p) end).
assert ( mx H, f mx (g mx H) = H) as f_g by (by intros ? [??]; subst).
intros p1 p2. rewrite <-(f_g _ p1), <-(f_g _ p2). by destruct mx, p1.
Qed.
Instance is_Some_dec {A} (x : option A) : Decision (is_Some x) :=
match x with
Instance is_Some_dec {A} (mx : option A) : Decision (is_Some mx) :=
match mx with
| Some x => left (ex_intro _ x eq_refl)
| None => right is_Some_None
end.
Definition is_Some_proj {A} {x : option A} : is_Some x A :=
match x with Some a => λ _, a | None => False_rect _ is_Some_None end.
Definition Some_dec {A} (x : option A) : { a | x = Some a } + { x = None } :=
match x return { a | x = Some a } + { x = None } with
| Some a => inleft (a eq_refl _)
Definition is_Some_proj {A} {mx : option A} : is_Some mx A :=
match mx with Some x => λ _, x | None => False_rect _ is_Some_None end.
Definition Some_dec {A} (mx : option A) : { x | mx = Some x } + { mx = None } :=
match mx return { x | mx = Some x } + { mx = None } with
| Some x => inleft (x eq_refl _)
| None => inright eq_refl
end.
Lemma eq_None_not_Some {A} (x : option A) : x = None ¬is_Some x.
Proof. destruct x; unfold is_Some; naive_solver. Qed.
Lemma not_eq_None_Some `(x : option A) : x None is_Some x.
Proof. rewrite eq_None_not_Some. split. apply dec_stable. tauto. Qed.
Lemma eq_None_not_Some {A} (mx : option A) : mx = None ¬is_Some mx.
Proof. destruct mx; unfold is_Some; naive_solver. Qed.
Lemma not_eq_None_Some {A} (mx : option A) : mx None is_Some mx.
Proof. rewrite eq_None_not_Some; apply dec_stable; tauto. Qed.
(** Lifting a relation point-wise to option *)
Inductive option_Forall2 {A B} (P: A B Prop) : option A option B Prop :=
......@@ -90,7 +95,12 @@ Definition option_relation {A B} (R: A → B → Prop) (P: A → Prop) (Q: B →
(** Setoids *)
Section setoids.
Context `{Equiv A} `{!Equivalence (() : relation A)}.
Global Instance option_equiv : Equiv (option A) := option_Forall2 ().
Lemma equiv_option_Forall2 mx my : mx my option_Forall2 () mx my.
Proof. split; destruct 1; constructor; auto. Qed.
Global Instance option_equivalence : Equivalence (() : relation (option A)).
Proof.
split.
......@@ -102,81 +112,86 @@ Section setoids.
Proof. by constructor. Qed.
Global Instance option_leibniz `{!LeibnizEquiv A} : LeibnizEquiv (option A).
Proof. intros x y; destruct 1; fold_leibniz; congruence. Qed.
Lemma equiv_None (mx : option A) : mx None mx = None.
Proof. split; [by inversion_clear 1|by intros ->]. Qed.
Lemma equiv_Some (mx my : option A) x :
Lemma equiv_Some_inv_l (mx my : option A) x :
mx my mx = Some x y, my = Some y x y.
Proof. destruct 1; naive_solver. Qed.
Lemma equiv_Some_inv_r (mx my : option A) y :
mx my mx = Some y x, mx = Some x x y.
Proof. destruct 1; naive_solver. Qed.
Global Instance is_Some_proper : Proper (() ==> iff) (@is_Some A).
Proof. inversion_clear 1; split; eauto. Qed.
Global Instance from_option_proper :
Proper (() ==> () ==> ()) (@from_option A).
Proof. by destruct 2. Qed.
End setoids.
(** Equality on [option] is decidable. *)
Instance option_eq_None_dec {A} (x : option A) : Decision (x = None) :=
match x with Some _ => right (Some_ne_None _) | None => left eq_refl end.
Instance option_None_eq_dec {A} (x : option A) : Decision (None = x) :=
match x with Some _ => right (None_ne_Some _) | None => left eq_refl end.
Instance option_eq_dec `{dec : x y : A, Decision (x = y)}
(x y : option A) : Decision (x = y).
Instance option_eq_None_dec {A} (mx : option A) : Decision (mx = None) :=
match mx with Some _ => right (Some_ne_None _) | None => left eq_refl end.
Instance option_None_eq_dec {A} (mx : option A) : Decision (None = mx) :=
match mx with Some _ => right (None_ne_Some _) | None => left eq_refl end.
Instance option_eq_dec {A} {dec : x y : A, Decision (x = y)}
(mx my : option A) : Decision (mx = my).
Proof.
refine
match x, y with
| Some a, Some b => cast_if (decide (a = b))
match mx, my with
| Some x, Some y => cast_if (decide (x = y))
| None, None => left _ | _, _ => right _
end; clear dec; abstract congruence.
Defined.
(** * Monadic operations *)
Instance option_ret: MRet option := @Some.
Instance option_bind: MBind option := λ A B f x,
match x with Some a => f a | None => None end.
Instance option_join: MJoin option := λ A x,
match x with Some x => x | None => None end.
Instance option_bind: MBind option := λ A B f mx,
match mx with Some x => f x | None => None end.
Instance option_join: MJoin option := λ A mmx,
match mmx with Some mx => mx | None => None end.
Instance option_fmap: FMap option := @option_map.
Instance option_guard: MGuard option := λ P dec A x,
match dec with left H => x H | _ => None end.
Instance option_guard: MGuard option := λ P dec A f,
match dec with left H => f H | _ => None end.
Lemma fmap_is_Some {A B} (f : A B) x : is_Some (f <$> x) is_Some x.
Proof. unfold is_Some; destruct x; naive_solver. Qed.
Lemma fmap_Some {A B} (f : A B) x y :
f <$> x = Some y x', x = Some x' y = f x'.
Proof. destruct x; naive_solver. Qed.
Lemma fmap_None {A B} (f : A B) x : f <$> x = None x = None.
Proof. by destruct x. Qed.
Lemma option_fmap_id {A} (x : option A) : id <$> x = x.
Proof. by destruct x. Qed.
Lemma option_fmap_compose {A B} (f : A B) {C} (g : B C) x :
g f <$> x = g <$> f <$> x.
Proof. by destruct x. Qed.
Lemma option_fmap_ext {A B} (f g : A B) x :
( y, f y = g y) f <$> x = g <$> x.
Proof. destruct x; simpl; auto with f_equal. Qed.
Lemma option_fmap_setoid_ext `{Equiv A, Equiv B} (f g : A B) x :
( y, f y g y) f <$> x g <$> x.
Proof. destruct x; constructor; auto. Qed.
Lemma option_fmap_bind {A B C} (f : A B) (g : B option C) x :
(f <$> x) = g = x = g f.
Proof. by destruct x. Qed.
Lemma fmap_is_Some {A B} (f : A B) mx : is_Some (f <$> mx) is_Some mx.
Proof. unfold is_Some; destruct mx; naive_solver. Qed.
Lemma fmap_Some {A B} (f : A B) mx y :
f <$> mx = Some y x, mx = Some x y = f x.
Proof. destruct mx; naive_solver. Qed.
Lemma fmap_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.
Proof. by destruct mx. Qed.
Lemma option_fmap_compose {A B} (f : A B) {C} (g : B C) mx :
g f <$> mx = g <$> f <$> mx.
Proof. by destruct mx. Qed.
Lemma option_fmap_ext {A B} (f g : A B) mx :
( x, f x = g x) f <$> mx = g <$> mx.
Proof. intros; destruct mx; f_equal/=; auto. Qed.
Lemma option_fmap_setoid_ext `{Equiv A, Equiv B} (f g : A B) mx :
( x, f x g x) f <$> mx g <$> mx.
Proof. destruct mx; constructor; auto. Qed.
Lemma option_fmap_bind {A B C} (f : A B) (g : B option C) mx :
(f <$> mx) = g = mx = g f.
Proof. by destruct mx. Qed.
Lemma option_bind_assoc {A B C} (f : A option B)
(g : B option C) (x : option A) : (x = f) = g = x = (mbind g f).
Proof. by destruct x; simpl. Qed.
Lemma option_bind_ext {A B} (f g : A option B) x y :
( a, f a = g a) x = y x = f = y = g.
Proof. intros. destruct x, y; simplify_eq; csimpl; auto. Qed.
Lemma option_bind_ext_fun {A B} (f g : A option B) x :
( a, f a = g a) x = f = x = g.
(g : B option C) (mx : option A) : (mx = f) = g = mx = (mbind g f).
Proof. by destruct mx; simpl. Qed.
Lemma option_bind_ext {A B} (f g : A option B) mx my :
( x, f x = g x) mx = my mx = f = my = g.
Proof. destruct mx, my; naive_solver. Qed.
Lemma option_bind_ext_fun {A B} (f g : A option B) mx :
( x, f x = g x) mx = f = mx = g.
Proof. intros. by apply option_bind_ext. Qed.
Lemma bind_Some {A B} (f : A option B) (x : option A) b :
x = f = Some b a, x = Some a f a = Some b.
Proof. split. by destruct x as [a|]; [exists a|]. by intros (?&->&?). Qed.
Lemma bind_None {A B} (f : A option B) (x : option A) :
x = f = None x = None a, x = Some a f a = None.
Proof.
split; [|by intros [->|(?&->&?)]].
destruct x; intros; simplify_eq/=; eauto.
Qed.
Lemma bind_with_Some {A} (x : option A) : x = Some = x.
Proof. by destruct x. Qed.
Lemma bind_Some {A B} (f : A option B) (mx : option A) y :
mx = f = Some y x, mx = Some x f x = Some y.
Proof. destruct mx; naive_solver. Qed.
Lemma bind_None {A B} (f : A option B) (mx : option A) :
mx = f = None mx = None x, mx = Some x f x = None.
Proof. destruct mx; naive_solver. Qed.
Lemma bind_with_Some {A} (mx : option A) : mx = Some = mx.
Proof. by destruct mx. Qed.
(** ** Inverses of constructors *)
(** We can do this in a fancy way using dependent types, but rewrite does
......@@ -206,25 +221,26 @@ Instance maybe_Some {A} : Maybe (@Some A) := id.
Arguments maybe_Some _ !_ /.
(** * Union, intersection and difference *)
Instance option_union_with {A} : UnionWith A (option A) := λ f x y,
match x, y with
| Some a, Some b => f a b
| Some a, None => Some a
| None, Some b => Some b
Instance option_union_with {A} : UnionWith A (option A) := λ f mx my,
match mx, my with
| Some x, Some y => f x y
| Some x, None => Some x
| None, Some y => Some y
| None, None => None
end.
Instance option_intersection_with {A} : IntersectionWith A (option A) :=
λ f x y, match x, y with Some a, Some b => f a b | _, _ => None end.
Instance option_difference_with {A} : DifferenceWith A (option A) := λ f x y,
match x, y with
| Some a, Some b => f a b
| Some a, None => Some a
λ f mx my, match mx, my with Some x, Some y => f x y | _, _ => None end.
Instance option_difference_with {A} : DifferenceWith A (option A) := λ f mx my,
match mx, my with
| Some x, Some y => f x y
| Some x, None => Some x
| None, _ => None
end.
Instance option_union {A} : Union (option A) := union_with (λ x _, Some x).
Lemma option_union_Some {A} (x y : option A) z :
x y = Some z x = Some z y = Some z.
Proof. destruct x, y; intros; simplify_eq; auto. Qed.
Lemma option_union_Some {A} (mx my : option A) z :
mx my = Some z mx = Some z my = Some z.
Proof. destruct mx, my; naive_solver. Qed.
Section option_union_intersection_difference.
Context {A} (f : A A option A).
......@@ -248,61 +264,61 @@ End option_union_intersection_difference.
Tactic Notation "case_option_guard" "as" ident(Hx) :=
match goal with
| H : appcontext C [@mguard option _ ?P ?dec] |- _ =>
change (@mguard option _ P dec) with (λ A (x : P option A),
match @decide P dec with left H' => x H' | _ => None end) in *;
change (@mguard option _ P dec) with (λ A (f : P option A),
match @decide P dec with left H' => f H' | _ => None end) in *;
destruct_decide (@decide P dec) as Hx
| |- appcontext C [@mguard option _ ?P ?dec] =>
change (@mguard option _ P dec) with (λ A (x : P option A),
match @decide P dec with left H' => x H' | _ => None end) in *;
change (@mguard option _ P dec) with (λ A (f : P option A),
match @decide P dec with left H' => f H' | _ => None end) in *;
destruct_decide (@decide P dec) as Hx
end.
Tactic Notation "case_option_guard" :=
let H := fresh in case_option_guard as H.
Lemma option_guard_True {A} P `{Decision P} (x : option A) :
P guard P; x = x.
Lemma option_guard_True {A} P `{Decision P} (mx : option A) :
P guard P; mx = mx.
Proof. intros. by case_option_guard. Qed.
Lemma option_guard_False {A} P `{Decision P} (x : option A) :
¬P guard P; x = None.
Lemma option_guard_False {A} P `{Decision P} (mx : option A) :
¬P guard P; mx = None.
Proof. intros. by case_option_guard. Qed.
Lemma option_guard_iff {A} P Q `{Decision P, Decision Q} (x : option A) :
(P Q) guard P; x = guard Q; x.
Lemma option_guard_iff {A} P Q `{Decision P, Decision Q} (mx : option A) :
(P Q) guard P; mx = guard Q; mx.
Proof. intros [??]. repeat case_option_guard; intuition. Qed.
Tactic Notation "simpl_option" "by" tactic3(tac) :=
let assert_Some_None A o H := first
let assert_Some_None A mx H := first
[ let x := fresh in evar (x:A); let x' := eval unfold x in x in clear x;
assert (o = Some x') as H by tac
| assert (o = None) as H by tac ]
assert (mx = Some x') as H by tac
| assert (mx = None) as H by tac ]
in repeat match goal with
| H : appcontext [@mret _ _ ?A] |- _ =>
change (@mret _ _ A) with (@Some A) in H
| |- appcontext [@mret _ _ ?A] => change (@mret _ _ A) with (@Some A)
| H : context [mbind (M:=option) (A:=?A) ?f ?o] |- _ =>
let Hx := fresh in assert_Some_None A o Hx; rewrite Hx in H; clear Hx
| H : context [fmap (M:=option) (A:=?A) ?f ?o] |- _ =>
let Hx := fresh in assert_Some_None A o Hx; rewrite Hx in H; clear Hx
| H : context [default (A:=?A) _ ?o _] |- _ =>
let Hx := fresh in assert_Some_None A o Hx; rewrite Hx in H; clear Hx
| H : context [from_option (A:=?A) _ ?o] |- _ =>
let Hx := fresh in assert_Some_None A o Hx; rewrite Hx in H; clear Hx
| H : context [ match ?o with _ => _ end ] |- _ =>
match type of o with
| H : context [mbind (M:=option) (A:=?A) ?f ?mx] |- _ =>
let Hx := fresh in assert_Some_None A mx Hx; rewrite Hx in H; clear Hx
| H : context [fmap (M:=option) (A:=?A) ?f ?mx] |- _ =>
let Hx := fresh in assert_Some_None A mx Hx; rewrite Hx in H; clear Hx
| H : context [default (A:=?A) _ ?mx _] |- _ =>
let Hx := fresh in assert_Some_None A mx Hx; rewrite Hx in H; clear Hx
| H : context [from_option (A:=?A) _ ?mx] |- _ =>
let Hx := fresh in assert_Some_None A mx Hx; rewrite Hx in H; clear Hx
| H : context [ match ?mx with _ => _ end ] |- _ =>
match type of mx with
| option ?A =>
let Hx := fresh in assert_Some_None A o Hx; rewrite Hx in H; clear Hx
let Hx := fresh in assert_Some_None A mx Hx; rewrite Hx in H; clear Hx
end
| |- context [mbind (M:=option) (A:=?A) ?f ?o] =>
let Hx := fresh in assert_Some_None A o Hx; rewrite Hx; clear Hx
| |- context [fmap (M:=option) (A:=?A) ?f ?o] =>
let Hx := fresh in assert_Some_None A o Hx; rewrite Hx; clear Hx
| |- context [default (A:=?A) _ ?o _] =>
let Hx := fresh in assert_Some_None A o Hx; rewrite Hx; clear Hx
| |- context [from_option (A:=?A) _ ?o] =>
let Hx := fresh in assert_Some_None A o Hx; rewrite Hx; clear Hx
| |- context [ match ?o with _ => _ end ] =>
match type of o with
| |- context [mbind (M:=option) (A:=?A) ?f ?mx] =>
let Hx := fresh in assert_Some_None A mx Hx; rewrite Hx; clear Hx
| |- context [fmap (M:=option) (A:=?A) ?f ?mx] =>
let Hx := fresh in assert_Some_None A mx Hx; rewrite Hx; clear Hx
| |- context [default (A:=?A) _ ?mx _] =>
let Hx := fresh in assert_Some_None A mx Hx; rewrite Hx; clear Hx
| |- context [from_option (A:=?A) _ ?mx] =>
let Hx := fresh in assert_Some_None A mx Hx; rewrite Hx; clear Hx
| |- context [ match ?mx with _ => _ end ] =>
match type of mx with
| option ?A =>
let Hx := fresh in assert_Some_None A o Hx; rewrite Hx; clear Hx
let Hx := fresh in assert_Some_None A mx Hx; rewrite Hx; clear Hx
end
| H : context [decide _] |- _ => rewrite decide_True in H by tac
| H : context [decide _] |- _ => rewrite decide_False in H by tac
......@@ -326,26 +342,26 @@ Tactic Notation "simplify_option_eq" "by" tactic3(tac) :=
| _ : maybe3 _ ?x = Some _ |- _ => is_var x; destruct x
| _ : maybe4 _ ?x = Some _ |- _ => is_var x; destruct x
| H : _ _ = Some _ |- _ => apply option_union_Some in H; destruct H
| H : mbind (M:=option) ?f ?o = ?x |- _ =>
match o with Some _ => fail 1 | None => fail 1 | _ => idtac end;
match x with Some _ => idtac | None => idtac | _ => fail 1 end;
let y := fresh in destruct o as [y|] eqn:?;
[change (f y = x) in H|change (None = x) in H]
| H : ?x = mbind (M:=option) ?f ?o |- _ =>
match o with Some _ => fail 1 | None => fail 1 | _ => idtac end;
match x with Some _ => idtac | None => idtac | _ => fail 1 end;
let y := fresh in destruct o as [y|] eqn:?;
[change (x = f y) in H|change (x = None) in H]
| H : fmap (M:=option) ?f ?o = ?x |- _ =>
match o with Some _ => fail 1 | None => fail 1 | _ => idtac end;
match x with Some _ => idtac | None => idtac | _ => fail 1 end;
let y := fresh in destruct o as [y|] eqn:?;
[change (Some (f y) = x) in H|change (None = x) in H]
| H : ?x = fmap (M:=option) ?f ?o |- _ =>
match o with Some _ => fail 1 | None => fail 1 | _ => idtac end;
match x with Some _ => idtac | None => idtac | _ => fail 1 end;
let y := fresh in destruct o as [y|] eqn:?;
[change (x = Some (f y)) in H|change (x = None) in H]
| H : mbind (M:=option) ?f ?mx = ?my |- _ =>
match mx with Some _ => fail 1 | None => fail 1 | _ => idtac end;
match my with Some _ => idtac | None => idtac | _ => fail 1 end;
let x := fresh in destruct mx as [x|] eqn:?;
[change (f x = my) in H|change (None = my) in H]
| H : ?my = mbind (M:=option) ?f ?mx |- _ =>
match mx with Some _ => fail 1 | None => fail 1 | _ => idtac end;
match my with Some _ => idtac | None => idtac | _ => fail 1 end;
let x := fresh in destruct mx as [x|] eqn:?;
[change (my = f x) in H|change (my = None) in H]
| H : fmap (M:=option) ?f ?mx = ?my |- _ =>
match mx with Some _ => fail 1 | None => fail 1 | _ => idtac end;
match my with Some _ => idtac | None => idtac | _ => fail 1 end;
let x := fresh in destruct mx as [x|] eqn:?;
[change (Some (f x) = my) in H|change (None = my) in H]
| H : ?my = fmap (M:=option) ?f ?mx |- _ =>
match mx with Some _ => fail 1 | None => fail 1 | _ => idtac end;
match my with Some _ => idtac | None => idtac | _ => fail 1 end;
let x := fresh in destruct mx as [x|] eqn:?;
[change (my = Some (f x)) in H|change (my = None) in H]
| _ => progress case_decide
| _ => progress case_option_guard
end.
......
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