3418d6db8e
This PR fixes an issue with the generation of equational theorems from `partial_fixpoint` when case-splitting is necessary. Fixes #6786.
101 lines
1.9 KiB
Text
101 lines
1.9 KiB
Text
def find42 : Nat → Bool
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| 42 => true
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| n => find42 (n + 1)
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partial_fixpoint
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/--
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info: find42.eq_def (x✝ : Nat) :
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find42 x✝ =
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match x✝ with
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| 42 => true
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| n => find42 (n + 1)
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-/
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#guard_msgs in
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#check find42.eq_def
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/--
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info: equations:
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theorem find42.eq_1 : find42 42 = true
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theorem find42.eq_2 : ∀ (x : Nat), (x = 42 → False) → find42 x = find42 (x + 1)
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-/
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#guard_msgs in
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#print equations find42
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mutual
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def find99 : Nat → Bool
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| 99 => true
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| n => find23 (n + 1)
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partial_fixpoint
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def find23 : Nat → Bool
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| 23 => true
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| n => find99 (n + 1)
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partial_fixpoint
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end
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/--
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info: find99.eq_def (x✝ : Nat) :
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find99 x✝ =
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match x✝ with
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| 99 => true
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| n => find23 (n + 1)
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-/
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#guard_msgs in
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#check find99.eq_def
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/--
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info: find23.eq_def (x✝ : Nat) :
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find23 x✝ =
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match x✝ with
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| 23 => true
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| n => find99 (n + 1)
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-/
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#guard_msgs in
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#check find23.eq_def
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/--
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info: equations:
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theorem find99.eq_1 : find99 99 = true
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theorem find99.eq_2 : ∀ (x : Nat), (x = 99 → False) → find99 x = find23 (x + 1)
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-/
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#guard_msgs in
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#print equations find99
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/--
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info: equations:
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theorem find23.eq_1 : find23 23 = true
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theorem find23.eq_2 : ∀ (x : Nat), (x = 23 → False) → find23 x = find99 (x + 1)
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-/
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#guard_msgs in
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#print equations find23
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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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partial_fixpoint
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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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partial_fixpoint
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end
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/--
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info: equations:
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theorem g.eq_1 : ∀ (i : Nat), g i Nat.zero = if i < 5 then 0 else 1
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theorem 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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-/
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#guard_msgs in
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#print equations g
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/--
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info: equations:
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theorem h.eq_1 : ∀ (i : Nat), h i 0 = g i 0
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theorem h.eq_2 : ∀ (i j_2 : Nat), h i j_2.succ = g i j_2
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-/
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#guard_msgs in
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#print equations h
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