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.
216 lines
5.6 KiB
Text
216 lines
5.6 KiB
Text
set_option trace.grind.ematch.pattern true
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attribute [grind =] Array.size_set
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set_option grind.debug true
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example (as bs : Array α) (v : α)
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(i : Nat)
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(h₁ : i < as.size)
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(h₂ : bs = as.set i v)
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: as.size = bs.size := by
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grind
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example (as bs : Array α) (v : α)
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(i : Nat)
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(h₁ : i < as.size)
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(h₂ : bs = as.set i v)
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: as.size = bs.size := by
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have : as.size = bs.size := by
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grind
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exact this
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set_option trace.grind.ematch.instance true
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attribute [grind =] Array.getElem_set_ne
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/--
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info: [grind.ematch.instance] Array.size_set: (as.set i v ⋯).size = as.size
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[grind.ematch.instance] Array.getElem_set_ne: ∀ (pj : j < as.size), i ≠ j → (as.set i v ⋯)[j] = as[j]
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-/
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#guard_msgs (info) in
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example (as bs cs : Array α) (v : α)
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(i : Nat)
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(h₁ : i < as.size)
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(h₂ : bs = as.set i v)
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(h₃ : cs = bs)
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(h₄ : i ≠ 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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opaque R : Nat → Nat → Prop
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theorem Rtrans (a b c : Nat) : R a b → R b c → R a c := sorry
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grind_pattern Rtrans => R a b, R b c
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/--
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info: [grind.ematch.instance] Rtrans: R a b → R b c → R a c
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-/
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#guard_msgs (info) in
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example : R a b → R b c → R a c := by
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grind
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/--
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info: [grind.ematch.instance] Rtrans: R a d → R d e → R a e
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[grind.ematch.instance] Rtrans: R c d → R d e → R c e
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[grind.ematch.instance] Rtrans: R b c → R c d → R b d
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[grind.ematch.instance] Rtrans: R a b → R b c → R a c
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[grind.ematch.instance] Rtrans: R a c → R c d → R a d
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[grind.ematch.instance] Rtrans: R a c → R c e → R a e
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[grind.ematch.instance] Rtrans: R b d → R d e → R b e
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[grind.ematch.instance] Rtrans: R a b → R b d → R a d
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[grind.ematch.instance] Rtrans: R b c → R c e → R b e
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-/
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#guard_msgs (info) in
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example : R a b → R b c → R c d → R d e → R a d := by
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grind
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namespace using_grind_fwd
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opaque S : Nat → Nat → Prop
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/--
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error: `@[grind →] theorem using_grind_fwd.StransBad` failed to find patterns in the antecedents of the theorem, consider using different options or the `grind_pattern` command
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-/
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#guard_msgs (error) in
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@[grind→] theorem StransBad (a b c d : Nat) : S a b ∨ R a b → S b c → S a c ∧ S b d := sorry
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set_option trace.grind.ematch.pattern.search true in
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/--
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info: [grind.ematch.pattern.search] candidate: S a b
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[grind.ematch.pattern.search] found pattern: S #4 #3
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[grind.ematch.pattern.search] candidate: R a b
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[grind.ematch.pattern.search] skip, no new variables covered
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[grind.ematch.pattern.search] candidate: S b c
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[grind.ematch.pattern.search] found pattern: S #3 #2
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[grind.ematch.pattern.search] found full coverage
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[grind.ematch.pattern] Strans: [S #4 #3, S #3 #2]
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-/
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#guard_msgs (info) in
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@[grind→] theorem Strans (a b c : Nat) : S a b ∨ R a b → S b c → S a c := sorry
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/--
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info: [grind.ematch.instance] Strans: S a b ∨ R a b → S b c → S a c
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-/
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#guard_msgs (info) in
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example : S a b → S b c → S a c := by
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grind
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end using_grind_fwd
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namespace using_grind_bwd
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opaque P : Nat → Prop
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opaque Q : Nat → Prop
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opaque f : Nat → Nat → Nat
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/-- info: [grind.ematch.pattern] pqf: [f #2 #1] -/
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#guard_msgs (info) in
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@[grind←] theorem pqf : Q x → P (f x y) := sorry
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/--
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info: [grind.ematch.instance] pqf: Q a → P (f a b)
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-/
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#guard_msgs (info) in
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example : Q 0 → Q 1 → Q 2 → Q 3 → ¬ P (f a b) → a = 1 → False := by
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grind
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end using_grind_bwd
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namespace using_grind_fwd2
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opaque P : Nat → Prop
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opaque Q : Nat → Prop
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opaque f : Nat → Nat → Nat
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/--
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error: `@[grind →] theorem using_grind_fwd2.pqfBad` failed to find patterns in the antecedents of the theorem, consider using different options or the `grind_pattern` command
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-/
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#guard_msgs (error) in
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@[grind→] theorem pqfBad : Q x → P (f x y) := sorry
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/--
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info: [grind.ematch.pattern] pqf: [Q #1]
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-/
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#guard_msgs (info) in
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@[grind→] theorem pqf : Q x → P (f x x) := sorry
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/--
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info: [grind.ematch.instance] pqf: Q 3 → P (f 3 3)
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[grind.ematch.instance] pqf: Q 2 → P (f 2 2)
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[grind.ematch.instance] pqf: Q 1 → P (f 1 1)
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[grind.ematch.instance] pqf: Q 0 → P (f 0 0)
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-/
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#guard_msgs (info) in
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example : Q 0 → Q 1 → Q 2 → Q 3 → ¬ P (f a a) → a = 1 → False := by
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grind
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end using_grind_fwd2
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namespace using_grind_mixed
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opaque P : Nat → Nat → Prop
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opaque Q : Nat → Nat → Prop
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/--
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error: `@[grind →] theorem using_grind_mixed.pqBad1` failed to find patterns in the antecedents of the theorem, consider using different options or the `grind_pattern` command
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-/
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#guard_msgs (error) in
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@[grind→] theorem pqBad1 : P x y → Q x z := sorry
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/--
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error: `@[grind ←] theorem using_grind_mixed.pqBad2` failed to find patterns in the theorem's conclusion, consider using different options or the `grind_pattern` command
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-/
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#guard_msgs (error) in
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@[grind←] theorem pqBad2 : P x y → Q x z := sorry
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/--
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info: [grind.ematch.pattern] pqBad: [Q #3 #1, P #3 #2]
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-/
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#guard_msgs (info) in
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@[grind] theorem pqBad : P x y → Q x z := sorry
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example : P a b → Q a c := by
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grind
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end using_grind_mixed
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namespace using_grind_rhs
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opaque f : Nat → Nat
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opaque g : Nat → Nat → Nat
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/--
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info: [grind.ematch.pattern] fq: [g #0 (f #0)]
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-/
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#guard_msgs (info) in
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@[grind =_]
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theorem fq : f x = g x (f x) := sorry
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end using_grind_rhs
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namespace using_grind_lhs_rhs
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opaque f : Nat → Nat
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opaque g : Nat → Nat → Nat
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/--
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info: [grind.ematch.pattern] fq: [f #0]
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[grind.ematch.pattern] fq: [g #0 (g #0 #0)]
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-/
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#guard_msgs (info) in
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@[grind _=_]
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theorem fq : f x = g x (g x x) := sorry
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end using_grind_lhs_rhs
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-- the following should still work
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#check _=_
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