145 lines
3.9 KiB
Text
145 lines
3.9 KiB
Text
module
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reset_grind_attrs%
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attribute [grind =] List.length_cons
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attribute [grind =] List.getElem?_eq_getElem
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attribute [grind =] List.length_replicate
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attribute [grind =] List.getElem_replicate
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attribute [grind =] List.getElem?_eq_none
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attribute [grind =] List.getElem?_eq_some_iff
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attribute [grind =] getElem!_pos
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attribute [grind =] Option.map_some Option.map_none
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attribute [grind =] List.getElem?_map
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attribute [grind =] List.getElem?_replicate
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attribute [grind =] List.getLast?_eq_some_iff
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attribute [grind ←] List.mem_concat_self
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attribute [grind =] List.getElem_cons_zero in
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attribute [grind =] List.getElem?_cons_zero in
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/--
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info: Try these:
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[apply] grind only [= List.getElem?_replicate]
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[apply] grind => instantiate only [= List.getElem?_replicate]
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-/
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#guard_msgs (info) in
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theorem getElem?_replicate' : (List.replicate n a)[m]? = if m < n then some a else none := by
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grind?
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/--
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info: Try these:
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[apply] grind only [= List.length_cons]
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[apply] grind => instantiate only [= List.length_cons]
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-/
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#guard_msgs (info) in
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example : 0 < (x :: t).length := by
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grind?
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attribute [grind ext] List.ext_getElem?
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/--
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info: Try these:
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[apply] grind only [= List.getElem?_replicate, = List.getElem?_map, = List.getElem?_eq_none,
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= List.getElem?_eq_getElem, = List.length_replicate, = List.getElem?_eq_some_iff, = Option.map_some,
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= Option.map_none, #12fe, #986e, #0323]
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[apply] grind only [= List.getElem?_replicate, = List.getElem?_map, = List.getElem?_eq_none,
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= List.getElem?_eq_getElem, = List.length_replicate, = List.getElem?_eq_some_iff, = Option.map_some,
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= Option.map_none]
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[apply] grind =>
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cases #12fe
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instantiate only [= List.getElem?_replicate, = List.getElem?_map, = List.getElem?_eq_none,
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= List.getElem?_eq_getElem]
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instantiate only [= List.getElem?_replicate, = List.getElem?_eq_none, = List.getElem?_eq_getElem,
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= List.length_replicate]
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instantiate only [= List.length_replicate]
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cases #986e
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· instantiate only [= List.getElem?_eq_some_iff]
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cases #0323
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· instantiate only [= Option.map_some]
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· instantiate only [= Option.map_none]
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· instantiate only [= Option.map_some]
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-/
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#guard_msgs (info) in
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theorem map_replicate' : (List.replicate n a).map f = List.replicate n (f a) := by
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grind?
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/--
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info: Try these:
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[apply] grind only [= List.getLast?_eq_some_iff, ← List.mem_concat_self, #e8ab]
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[apply] grind only [= List.getLast?_eq_some_iff, ← List.mem_concat_self]
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[apply] grind =>
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instantiate only [= List.getLast?_eq_some_iff]
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cases #e8ab <;> instantiate only [← List.mem_concat_self]
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-/
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#guard_msgs (info) 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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@[expose] public def f : Nat → Nat
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| 0 => 1
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| _ => 2
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/--
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info: Try these:
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[apply] grind only
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[apply] grind => instantiate only
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-/
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#guard_msgs (info) in
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example : x = 0 → f x = 1 := by
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unfold f
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grind? -- should not include match equations
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attribute [grind] f
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/--
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info: Try these:
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[apply] grind only [f]
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[apply] grind => instantiate only [f]
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-/
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#guard_msgs (info) in
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example : x = 0 → f x = 1 := by
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grind? [f]
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opaque g : Nat → Nat
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theorem gthm : g (g x) = g x := sorry
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grind_pattern gthm => g (g x)
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/--
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info: Try these:
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[apply] grind only [usr gthm]
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[apply] grind => instantiate only [usr gthm]
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-/
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#guard_msgs (info) in
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example : g (g (g x)) = g x := by
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grind?
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/--
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error: `And` is marked as a built-in case-split for `grind` and cannot be erased
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-/
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#guard_msgs (error) in
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attribute [-grind] And
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/--
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error: `And` is marked as a built-in case-split for `grind` and cannot be erased
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-/
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#guard_msgs (error) in
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example : p ∧ q → p := by
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grind [-And]
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example : (List.replicate n a)[m]? = if m < n then some a else none := by
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grind?
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reset_grind_attrs%
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set_option warn.sorry false
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/--
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info: Try these:
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[apply] grind => sorry
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-/
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#guard_msgs in
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example : (List.replicate n a)[m]? = if m < n then some a else none := by
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grind?
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