cf3b257ccd
This PR cleans up the `Option` development, upstreaming some results from mathlib in the process. Notable changes: - the name `<op>_eq_some_iff` is preferred over `<op>_eq_some` - the `simp` normal form for `<$>` is `Option.map`, for `>>=` is `Option.bind` and for `<|>` is `Option.orElse` (for the former two, this was already true before this PR). All further lemmas about these operations are now stated only in terms of `Option.map`/`Option.bind`/`Option.orElse`. Previously, in some cases both versions were available, with a prime used to disambiguate (the primed version was usually the "non-ascii-art" version). Now, there are no lemmas about the ascii-art versions besides the ones turning them into the non-ascii-art operations, and there is only one version of every lemma, about the non-ascii-art operation, and named without a prime.
37 lines
1.2 KiB
Text
37 lines
1.2 KiB
Text
reset_grind_attrs%
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namespace List
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attribute [local grind =] List.length_cons in
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example : 0 < (x :: t).length := by grind
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attribute [local grind →] getElem?_eq_getElem in
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attribute [local grind =] length_replicate in
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attribute [local grind =] getElem_replicate in
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attribute [local grind =] getElem?_eq_none in
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theorem getElem?_replicate' : (replicate n a)[m]? = if m < n then some a else none := by
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grind
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attribute [local grind =] getElem?_eq_some_iff in
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attribute [local grind =] getElem!_pos in
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theorem getElem!_of_getElem?' [Inhabited α] :
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∀ {l : List α} {i : Nat}, l[i]? = some b → l[i]! = b := by
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grind
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attribute [local grind =] Option.map_some Option.map_none in
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attribute [local grind =] getElem?_map in
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attribute [local grind =] getElem?_replicate in
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theorem map_replicate' : (replicate n a).map f = replicate n (f a) := by
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grind?
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#print map_replicate'
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attribute [local grind =] getLast?_eq_some_iff in
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attribute [local grind] mem_concat_self in
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theorem mem_of_getLast?_eq_some' {xs : List α} {a : α} (h : xs.getLast? = some a) : a ∈ xs := by
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grind
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attribute [local grind =] getElem_cons_zero in
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attribute [local grind =] getElem?_cons_zero in
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example (h : (a :: t)[0]? = some b) : (a :: t)[0] = b := by
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grind
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