c8dae31ba5
This PR reviews `grind` annotations for `Option`, preferring to use `@[grind =]` instead of `@[grind]` (and fixing a few problems revealed by this), and making sure `@[grind =]` theorems are "fully applied".
58 lines
1.9 KiB
Text
58 lines
1.9 KiB
Text
-- This file uses `#guard_msgs` to check which lemmas `grind` is using.
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-- This may prove fragile, so remember it is okay to update the expected output if appropriate!
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-- Hopefully these will act as regression tests against `grind` activating irrelevant lemmas.
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section
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variable [BEq α] {o₁ o₂ o₃ o₄ o₅ : Option α}
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/--
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info: Try this: grind only [=_ Option.or_assoc, = Option.getD_or, = Option.or_some, = Option.some_beq_none, = Option.or_assoc,
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= Option.some_or]
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-/
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#guard_msgs in
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example : ((o₁.or (o₂.or (some x))).or (o₄.or o₅) == none) = false := by grind?
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/-- info: Try this: grind only [Option.max_none_right, Option.min_some_some, = Nat.min_def] -/
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#guard_msgs in
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example : max (some 7) none = min (some 13) (some 7) := by grind?
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/-- info: Try this: grind only [= Option.guard_apply] -/
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#guard_msgs in
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example : Option.guard (· ≤ 7) 3 = some 3 := by grind?
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/-- info: Try this: grind only [= Option.mem_bind_iff] -/
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#guard_msgs in
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example {x : β} {o : Option α} {f : α → Option β} (h : a ∈ o) (h' : x ∈ f a) : x ∈ o.bind f := by grind?
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end
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open Option
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theorem toList_toArray {o : Option α} : o.toArray.toList = o.toList := by
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grind
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theorem toArray_toList {o : Option α} : o.toList.toArray = o.toArray := by
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grind
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theorem size_toArray_eq_one_iff {o : Option α} :
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o.toArray.size = 1 ↔ o.isSome := by
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grind
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theorem size_toArray_choice_eq_one [Nonempty α] : (choice α).toArray.size = 1 := by
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grind
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theorem length_toList_eq_one_iff {o : Option α} :
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o.toList.length = 1 ↔ o.isSome := by
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grind
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theorem length_toList_choice_eq_one [Nonempty α] : (choice α).toList.length = 1 := by
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grind
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example : (default : Option α) = none := by grind
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example (a : α) : Option.all q (guard p a) = (!p a || q a) := by grind
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example (a : α) : Option.any q (guard p a) = (p a && q a) := by grind
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example : (guard p a).or (guard q a) = guard (fun x => p x || q x) a := by grind
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