4c9601e60f
This PR completes support for injective functions in grind. See
examples:
```lean
/-! Add some injectivity theorems. -/
def double (x : Nat) := 2*x
@[grind inj] theorem double_inj : Function.Injective double := by
grind [Function.Injective, double]
structure InjFn (α : Type) (β : Type) where
f : α → β
h : Function.Injective f
instance : CoeFun (InjFn α β) (fun _ => α → β) where
coe s := s.f
@[grind inj] theorem fn_inj (F : InjFn α β) : Function.Injective (F : α → β) := by
grind [Function.Injective, cases InjFn]
def toList (a : α) : List α := [a]
@[grind inj] theorem toList_inj : Function.Injective (toList : α → List α) := by
grind [Function.Injective, toList]
/-! Examples -/
example (x y : Nat) : toList (double x) = toList (double y) → x = y := by
grind
example (f : InjFn (List Nat) α) (x y z : Nat)
: f (toList (double x)) = f (toList y) →
y = double z →
x = z := by
grind
```
76 lines
2 KiB
Text
76 lines
2 KiB
Text
reset_grind_attrs%
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def succ (x : Nat) := x+1
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/-- trace: [grind.inj] succ_inj: [succ] -/
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#guard_msgs in
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set_option trace.grind.inj true in
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@[grind inj] theorem succ_inj : Function.Injective succ := by
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grind [Function.Injective, succ]
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/-- trace: [grind.debug.inj] [succ_inj] -/
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#guard_msgs in
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example : True := by
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set_option trace.grind.debug.inj true in
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grind
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/-- trace: [grind.debug.inj] [] -/
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#guard_msgs in
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example : True := by
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set_option trace.grind.debug.inj true in
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grind [- succ_inj]
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def double (x : Nat) := 2*x
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@[grind inj] theorem double_inj : Function.Injective double := by
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grind [Function.Injective, double]
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/-- trace: [grind.debug.inj] [double_inj, succ_inj] -/
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#guard_msgs in
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example : True := by
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set_option trace.grind.debug.inj true in
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grind
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attribute [- grind] succ_inj
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/-- error: `succ_inj` is not marked with the `[grind]` attribute -/
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#guard_msgs in
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example : True := by
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grind [- succ_inj]
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/--
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error: invalid `[grind inj]` theorem, resulting type is not of the form `Function.Injective <fun>`
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x = y
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-/
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#guard_msgs in
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@[grind inj] theorem succ_inj' : succ x = succ y → x = y := by
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grind [succ]
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/-- trace: [grind.inj] mul_2_inj: [HMul.hMul, OfNat.ofNat] -/
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#guard_msgs in
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set_option trace.grind.inj true in
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@[grind inj] theorem mul_2_inj : Function.Injective (2 * ·) := by
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grind [Function.Injective]
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def Array.IsId (as : Array Nat) : Prop :=
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∀ i : Fin as.size, as[i] = i
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/-- trace: [grind.inj] array_inj: [Array, GetElem?.getElem?, Fin, Array.size] -/
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#guard_msgs in
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set_option trace.grind.inj true in
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@[grind inj] theorem array_inj {as : Array Nat} (h : as.IsId) : Function.Injective (as[·]? : Fin as.size → Option Nat) := by
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intro a b; simp
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have ha := h a
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have hb := h b
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simp at ha hb
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grind
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def weird.{u} : PUnit.{u} → PUnit.{u} := id
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/--
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error: invalid `[grind inj]` theorem, theorem has universe levels, but no hypotheses
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Function.Injective weird
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-/
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#guard_msgs in
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@[grind inj] theorem weird_inj : Function.Injective weird := by
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intro a b; simp
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