604133d189
This PR takes Array-specific lemmas at the end of `Array/Lemmas.lean` (i.e. material that does not have exact correspondences with `List/Lemmas.lean`) and moves them to more appropriate homes. More to come.
111 lines
3.9 KiB
Text
111 lines
3.9 KiB
Text
attribute [grind =] Array.size_set Array.getElem_set_self Array.getElem_set_ne
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set_option grind.debug true
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set_option trace.grind.ematch.pattern true
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set_option trace.grind.ematch.instance true
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example (as bs cs : Array α) (v₁ v₂ : α)
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(i₁ i₂ j : Nat)
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(h₁ : i₁ < as.size)
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(h₂ : bs = as.set i₁ v₁)
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(h₃ : i₂ < bs.size)
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(h₃ : cs = bs.set i₂ v₂)
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(h₄ : i₁ ≠ j ∧ i₂ ≠ j)
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(h₅ : j < cs.size)
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(h₆ : j < as.size)
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: cs[j] = as[j] := by
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grind
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example (as bs cs : Array α) (v₁ v₂ : α)
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(i₁ i₂ j : Nat)
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(h₁ : i₁ < as.size)
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(h₂ : as.set i₁ v₁ = bs)
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(h₃ : i₂ < bs.size)
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(h₃ : bs.set i₂ v₂ = cs)
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(h₄ : i₁ ≠ j ∧ j ≠ i₂)
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(h₅ : j < cs.size)
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(h₆ : j < as.size)
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: cs[j] = as[j] := by
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grind
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example (as bs cs : Array α) (v₁ v₂ : α)
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(i₁ i₂ j : Nat)
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(h₁ : i₁ < as.size)
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(h₂ : as.set i₁ v₁ = bs)
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(h₃ : i₂ < bs.size)
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(h₃ : bs.set i₂ v₂ = cs)
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(h₄ : j ≠ i₁ ∧ j ≠ i₂)
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(h₅ : j < cs.size)
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(h₆ : j < as.size)
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: cs[j] = as[j] := by
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grind
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/--
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info: [grind] Diagnostics
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[thm] E-Matching instances
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[thm] Array.getElem_set_ne ↦ 3
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[thm] Array.size_set ↦ 3
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[grind] Simplifier
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[simp] tried theorems (max: 30, num: 2):
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[simp] eq_self ↦ 30 ❌️
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[simp] Lean.Grind.gt_eq ↦ 28 ❌️
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use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
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---
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info: [diag] Diagnostics
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[reduction] unfolded declarations (max: 11519, num: 3):
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[reduction] LT.lt ↦ 11519
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[reduction] getElem ↦ 76
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[reduction] Nat.lt ↦ 34
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[reduction] unfolded instances (max: 38, num: 1):
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[reduction] Array.instGetElemNatLtSize ↦ 38
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[reduction] unfolded reducible declarations (max: 6907, num: 7):
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[reduction] Array.size ↦ 6907
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[reduction] Array.toList ↦ 1851
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[reduction] autoParam ↦ 1675
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[reduction] outParam ↦ 168
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[reduction] Ne ↦ 60
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[reduction] GT.gt ↦ 46
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[reduction] List.casesOn ↦ 24
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[def_eq] heuristic for solving `f a =?= f b` (max: 4929, num: 2):
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[def_eq] Nat.lt ↦ 4929
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[def_eq] List.length ↦ 1645
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[kernel] unfolded declarations (max: 106, num: 5):
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[kernel] LT.lt ↦ 106
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[kernel] outParam ↦ 46
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[kernel] Array.size ↦ 36
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[kernel] Array.toList ↦ 31
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[kernel] autoParam ↦ 26
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use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
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---
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info: [grind.ematch.instance] Array.size_set: (cs.set i₃ v₃ ⋯).size = cs.size
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[grind.ematch.instance] Array.size_set: (bs.set i₂ v₂ ⋯).size = bs.size
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[grind.ematch.instance] Array.size_set: (as.set i₁ v₁ ⋯).size = as.size
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[grind.ematch.instance] Array.getElem_set_ne: ∀ (pj : j < cs.size), i₃ ≠ j → (cs.set i₃ v₃ ⋯)[j] = cs[j]
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[grind.ematch.instance] Array.getElem_set_ne: ∀ (pj : j < bs.size), i₂ ≠ j → (bs.set i₂ v₂ ⋯)[j] = bs[j]
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[grind.ematch.instance] Array.getElem_set_ne: ∀ (pj : j < as.size), i₁ ≠ j → (as.set i₁ v₁ ⋯)[j] = as[j]
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-/
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#guard_msgs (info) in
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example (as bs cs ds : Array α) (v₁ v₂ v₃ : α)
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(i₁ i₂ i₃ j : Nat)
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(h₁ : i₁ < as.size)
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(h₂ : as.set i₁ v₁ = bs)
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(h₃ : i₂ < bs.size)
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(h₃ : bs.set i₂ v₂ = cs)
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(h₄ : i₃ < cs.size)
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(h₅ : ds = cs.set i₃ v₃)
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(h₆ : j ≠ i₁ ∧ j ≠ i₂ ∧ i₃ ≠ j)
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(h₇ : j < ds.size)
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(h₈ : j < as.size)
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: ds[j] = as[j] := by
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set_option diagnostics true in
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grind
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opaque f (a b : α) : α := a
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@[grind =] theorem fx : f x (f x x) = x := sorry
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/--
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info: [grind.ematch.instance] fx: f a (f a a) = a
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-/
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#guard_msgs (info) in
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example : a = b₁ → c = f b₁ b₂ → f a c ≠ a → a = b₂ → False := by
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grind
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