64 lines
991 B
Text
64 lines
991 B
Text
namespace Ex1
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mutual
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def h (c : Nat) (x : Nat) := match g c x c c with
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| 0 => 1
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| r => r + 2
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termination_by 0
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decreasing_by all_goals sorry
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def g (c : Nat) (t : Nat) (a b : Nat) : Nat := match t with
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| (n+1) => match g c n a b with
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| 0 => 0
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| m => match g c (n - m) a b with
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| 0 => 0
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| m + 1 => g c m a b
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| 0 => f c 0
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termination_by 0
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decreasing_by all_goals sorry
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def f (c : Nat) (x : Nat) := match h c x with
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| 0 => 1
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| r => f c r
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termination_by 0
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decreasing_by all_goals sorry
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end
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attribute [simp] g
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attribute [simp] h
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attribute [simp] f
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#check g.eq_1
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#check g.eq_2
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#check h.eq_1
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#check f.eq_1
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end Ex1
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namespace Ex2
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def g (t : Nat) : Nat := match t with
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| (n+1) => match g n with
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| 0 => 0
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| m + 1 => match g (n - m) with
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| 0 => 0
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| m + 1 => g n
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| 0 => 0
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decreasing_by all_goals sorry
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theorem ex1 : g 0 = 0 := by
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rw [g]
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#check g.eq_1
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#check g.eq_2
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theorem ex2 : g 0 = 0 := by
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unfold g
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simp
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#check g.def
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end Ex2
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