24 lines
581 B
Text
24 lines
581 B
Text
def g (x : Nat) (b : Bool) :=
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if b then
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x - 1
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else
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x + 1
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theorem g_eq (x : Nat) (h : ¬ x = 0) : g x (x > 0) = x - 1 ∧ g x false = x + 1 := by
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have : x > 0 := by match x with
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| 0 => contradiction
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| x+1 => apply Nat.zero_lt_succ
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simp [g, this]
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macro_rules
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| `(tactic| decreasing_tactic) =>
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`(tactic|
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(simp [invImage, InvImage, Prod.lex, sizeOfWFRel, measure, Nat.lt_wfRel, WellFoundedRelation.rel, g_eq, *]
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apply Nat.pred_lt; assumption))
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def f (x : Nat) : Nat :=
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if h : x = 0 then
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1
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else
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f (g x (x > 0)) + 2
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termination_by f x => x
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