b2ed6ac939
This PR adds an `foo._unary.eq_def` theorem, so that unfolding `foo._unary` works as expected. This will help with #8019.
99 lines
2.6 KiB
Text
99 lines
2.6 KiB
Text
mutual
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def f : Nat → α → α → α
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| 0, a, b => a
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| n, a, b => g a n b |>.1
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termination_by n _ _ => (n, 2)
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decreasing_by
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apply Prod.Lex.right
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decide
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def g : α → Nat → α → (α × α)
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| a, 0, b => (a, b)
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| a, n, b => (h a b n, a)
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termination_by _ n _ => (n, 1)
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decreasing_by
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apply Prod.Lex.right
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decide
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def h : α → α → Nat → α
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| a, b, 0 => b
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| a, b, n+1 => f n a b
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termination_by _ _ n => (n, 0)
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decreasing_by
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apply Prod.Lex.left
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apply Nat.lt_succ_self
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end
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/-- info: 'a' -/
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#guard_msgs in
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#eval f 5 'a' 'b'
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/-- info: @f.eq_1 : ∀ {α : Type u_1} (x x_1 : α), f 0 x x_1 = x -/
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#guard_msgs in
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#check @f.eq_1
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/--
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info: @f.eq_2 : ∀ {α : Type u_1} (x : Nat) (x_1 x_2 : α), (x = 0 → False) → f x x_1 x_2 = (g x_1 x x_2).fst
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-/
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#guard_msgs in
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#check @f.eq_2
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/--
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info: @f.eq_def : ∀ {α : Type u_1} (x : Nat) (x_1 x_2 : α),
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f x x_1 x_2 =
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match x, x_1, x_2 with
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| 0, a, b => a
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| n, a, b => (g a n b).fst
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-/
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#guard_msgs in
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#check @f.eq_def
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/-- error: unknown identifier 'f.eq_3' -/
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#guard_msgs in
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#check @f.eq_3
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/-- info: @h.eq_1 : ∀ {α : Type u_1} (x x_1 : α), h x x_1 0 = x_1 -/
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#guard_msgs in
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#check @h.eq_1
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/-- info: @h.eq_2 : ∀ {α : Type u_1} (x x_1 : α) (n : Nat), h x x_1 n.succ = f n x x_1 -/
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#guard_msgs in
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#check @h.eq_2
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/--
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info: @h.eq_def : ∀ {α : Type u_1} (x x_1 : α) (x_2 : Nat),
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h x x_1 x_2 =
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match x, x_1, x_2 with
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| a, b, 0 => b
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| a, b, n.succ => f n a b
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-/
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#guard_msgs in
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#check @h.eq_def
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/-- error: unknown identifier 'h.eq_3' -/
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#guard_msgs in
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#check @h.eq_3
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/--
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info: f._mutual.eq_def.{u_1} {α : Type u_1}
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(x✝ : (_ : Nat) ×' (_ : α) ×' α ⊕' (_ : α) ×' (_ : Nat) ×' α ⊕' (_ : α) ×' (_ : α) ×' Nat) :
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f._mutual x✝ =
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PSum.casesOn x✝
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(fun _x =>
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PSigma.casesOn _x fun a a_1 =>
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PSigma.casesOn a_1 fun a_2 a_3 =>
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match a, a_2, a_3 with
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| 0, a, b => a
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| n, a, b => (f._mutual (PSum.inr (PSum.inl ⟨a, ⟨n, b⟩⟩))).fst)
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fun _x =>
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PSum.casesOn _x
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(fun _x =>
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PSigma.casesOn _x fun a a_1 =>
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PSigma.casesOn a_1 fun a_2 a_3 =>
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match a, a_2, a_3 with
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| a, 0, b => (a, b)
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| a, n, b => (f._mutual (PSum.inr (PSum.inr ⟨a, ⟨b, n⟩⟩)), a))
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fun _x =>
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PSigma.casesOn _x fun a a_1 =>
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PSigma.casesOn a_1 fun a_2 a_3 =>
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match a, a_2, a_3 with
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| a, b, 0 => b
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| a, b, n.succ => f._mutual (PSum.inl ⟨n, ⟨a, b⟩⟩)
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-/
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#guard_msgs in
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#check f._mutual.eq_def
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