19eac5f341
This PR ensures that the configuration in `Simp.Config` is used when reducing terms and checking definitional equality in `simp`. closes #5455 --------- Co-authored-by: Kim Morrison <kim@tqft.net>
36 lines
1.5 KiB
Text
36 lines
1.5 KiB
Text
example {α β : Type} {f : α × β → β → β} (h : ∀ p : α × β, f p p.2 = p.2)
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(a : α) (b : β) : f (a, b) b = b := by
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simp [h] -- should not fail
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example {α β : Type} {f : α × β → β → β}
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(a : α) (b : β) (h : f (a,b) (a,b).2 = (a,b).2) : f (a, b) b = b := by
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simp [h] -- should not fail
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def enumFromTR' (n : Nat) (l : List α) : List (Nat × α) :=
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let arr := l.toArray
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(arr.foldr (fun a (n, acc) => (n-1, (n-1, a) :: acc)) (n + arr.size, [])).2
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open List in
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theorem enumFrom_eq_enumFromTR' : @enumFrom = @enumFromTR' := by
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funext α n l; simp only [enumFromTR']
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let f := fun (a : α) (n, acc) => (n-1, (n-1, a) :: acc)
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let rec go : ∀ l n, l.foldr f (n + l.length, []) = (n, enumFrom n l)
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| [], n => rfl
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| a::as, n => by
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rw [← show _ + as.length = n + (a::as).length from Nat.succ_add .., List.foldr, go as]
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simp [enumFrom, f]
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rw [←Array.foldr_toList]
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simp [f] at go -- We must unfold `f` at `go`, or use `+zetaDelta`. See next theorem
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simp [go]
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open List in
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theorem enumFrom_eq_enumFromTR'' : @enumFrom = @enumFromTR' := by
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funext α n l; simp only [enumFromTR']
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let f := fun (a : α) (n, acc) => (n-1, (n-1, a) :: acc)
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let rec go : ∀ l n, l.foldr f (n + l.length, []) = (n, enumFrom n l)
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| [], n => rfl
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| a::as, n => by
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rw [← show _ + as.length = n + (a::as).length from Nat.succ_add .., List.foldr, go as]
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simp [enumFrom, f]
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rw [←Array.foldr_toList]
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simp +zetaDelta [go]
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