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[Merged by Bors] - feat(data/option/basic): lemmas on map of none and congr #5424

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[Merged by Bors] - feat(data/option/basic): lemmas on map of none and congr #5424

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12 changes: 12 additions & 0 deletions src/data/option/basic.lean
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Expand Up @@ -106,6 +106,18 @@ by cases x; simp
x.map f = some b ↔ ∃ a, x = some a ∧ f a = b :=
by cases x; simp

lemma map_eq_none {α β} {x : option α} {f : α → β} :
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Suggested change
lemma map_eq_none {α β} {x : option α} {f : α → β} :
@[simp] lemma map_eq_none {α β} {x : option α} {f : α → β} :

like below? Or is there a reason not to?

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simp linter complains if both are simp afair.

f <$> x = none ↔ x = none :=
by { cases x; simp only [map_none, map_some, eq_self_iff_true] }

@[simp] lemma map_eq_none' {x : option α} {f : α → β} :
x.map f = none ↔ x = none :=
by { cases x; simp only [map_none', map_some', eq_self_iff_true] }

lemma map_congr {f g : α → β} {x : option α} (h : ∀ a ∈ x, f a = g a) :
option.map f x = option.map g x :=
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I think this lemma would be better if you left it without the x in the result (and maybe also the hypothesis. If you do that, then you can claim that map is injective

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@pechersky pechersky Dec 19, 2020 •
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How would you phrase the hypothesis then? I've found this lemma useful for the cases when x is some complex expression, and f a = g a for all some a for that complex x, but not in the general case.

There's already an option.map_injective lemma.

by { cases x; simp only [map_none', map_some', h, mem_def] }

@[simp] theorem map_id' : option.map (@id α) = id := map_id

@[simp] lemma map_map (h : β → γ) (g : α → β) (x : option α) :
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