b2ed6ac939
This PR adds an `foo._unary.eq_def` theorem, so that unfolding `foo._unary` works as expected. This will help with #8019.
87 lines
1.6 KiB
Text
87 lines
1.6 KiB
Text
mutual
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def g (i j : Nat) : Nat :=
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if i < 5 then 0 else
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match j with
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| Nat.zero => 1
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| Nat.succ j => h i j
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termination_by (i + j, 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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def h (i j : Nat) : Nat :=
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match j with
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| 0 => g i 0
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| Nat.succ j => g i j
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termination_by (i + j, 1)
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decreasing_by
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· apply Prod.Lex.right
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decide
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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: g.eq_1 (i : Nat) : g i Nat.zero = if i < 5 then 0 else 1 -/
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#guard_msgs in
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#check g.eq_1
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/-- info: g.eq_2 (i j_2 : Nat) : g i j_2.succ = if i < 5 then 0 else h i j_2 -/
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#guard_msgs in
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#check g.eq_2
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/--
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info: g.eq_def (i j : Nat) :
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g i j =
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if i < 5 then 0
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else
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match j with
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| Nat.zero => 1
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| j.succ => h i j
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-/
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#guard_msgs in
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#check g.eq_def
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/-- error: unknown identifier 'g.eq_3' -/
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#guard_msgs in
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#check g.eq_3
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/-- info: h.eq_1 (i : Nat) : h i 0 = g i 0 -/
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#guard_msgs in
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#check h.eq_1
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/-- info: h.eq_2 (i j_2 : Nat) : h i j_2.succ = g i j_2 -/
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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 (i j : Nat) :
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h i j =
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match j with
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| 0 => g i 0
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| j.succ => g i j
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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: g._mutual.eq_def (i : Nat) (x✝ : Nat ⊕' Nat) :
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g._mutual i x✝ =
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PSum.casesOn x✝
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(fun j =>
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if i < 5 then 0
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else
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match j with
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| Nat.zero => 1
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| j.succ => g._mutual i (PSum.inr j))
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fun j =>
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match j with
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| 0 => g._mutual i (PSum.inl 0)
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| j.succ => g._mutual i (PSum.inl j)
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-/
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#guard_msgs in
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#check g._mutual.eq_def
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