3dd12f85f0
This PR adds further `@[grind]` annotations for `Option`, as follow-up to the recent additions to the `Option` API in #8379 and #8298. **However**, I am concurrently investigating adding `attribute [grind cases] Option`, which will result in many (most?) of the annotations for `Option` being removed again. In any case, I'm going to merge this first, as if that is viable I would like to test that most/all the lemmas now marked with `@[grind]` are still provable by `grind`.
44 lines
1.5 KiB
Text
44 lines
1.5 KiB
Text
open Option
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set_option grind.warning false
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-- TODO: the following lemmas currently fail, but could be solved with some subset of the following attributes:
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-- I haven't added them yet, because the nuclear option of `[grind cases]` is tempting, but a bit scary.
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attribute [grind] Option.eq_none_of_isNone
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attribute [grind] Option.toArray_eq_empty_iff
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attribute [grind] Option.toList_eq_nil_iff
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attribute [grind cases] Option
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theorem toArray_eq_empty_iff {o : Option α} : o.toArray = #[] ↔ o = none := by
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grind
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theorem toArray_eq_singleton_iff {o : Option α} : o.toArray = #[a] ↔ o = some a := by
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grind
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theorem size_toArray_eq_zero_iff {o : Option α} :
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o.toArray.size = 0 ↔ o = none := by
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grind
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theorem toList_eq_nil_iff {o : Option α} : o.toList = [] ↔ o = none := by
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grind
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theorem toList_eq_singleton_iff {o : Option α} : o.toList = [a] ↔ o = some a := by
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grind
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theorem length_toList_eq_zero_iff {o : Option α} :
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o.toList.length = 0 ↔ o = none := by
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grind
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attribute [grind] Std.IdempotentOp -- Lots more of these!
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example [Max α] [Std.IdempotentOp (α := α) max] {p : α → Bool} {o : Option α} :
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max (o.filter p) o = o := by grind
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example [Max α] [Std.IdempotentOp (α := α) max] {o : Option α} {p : (a : α) → o = some a → Bool} :
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max (o.pfilter p) o = o := by grind
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example [Max α] {o o' : Option α} : (max o o').isSome = (o.isSome || o'.isSome) := by grind
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example [Max α] {o o' : Option (Option α)} : (max o o').join = max o.join o'.join := by grind
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