42 lines
942 B
Text
42 lines
942 B
Text
def f (x y z : Nat) : Nat :=
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match x, y, z with
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| 5, _, _ => y
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| _, 5, _ => y
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| _, _, 5 => y
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| _, _, _ => 1
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example (x y z : Nat) : x ≠ 5 → y ≠ 5 → z ≠ 5 → f x y z = 1 := by
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intros
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simp [f]
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split
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. contradiction
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. contradiction
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. contradiction
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. rfl
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example (x y z : Nat) : f x y z = y ∨ f x y z = 1 := by
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intros
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simp [f]
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split
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. exact Or.inl rfl
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. exact Or.inl rfl
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. exact Or.inl rfl
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. exact Or.inr rfl
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example (x y z : Nat) : f x y z = y ∨ f x y z = 1 := by
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intros
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simp [f]
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split <;> (first | apply Or.inl rfl | apply Or.inr rfl)
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def g (xs ys : List Nat) : Nat :=
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match xs, ys with
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| [a, b], _ => Nat.succ (a+b)
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| _, [b, c] => Nat.succ b
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| _, _ => 1
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example (xs ys : List Nat) : g xs ys > 0 := by
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simp [g]
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split
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next a b _ => show Nat.succ (a + b) > 0; apply Nat.zero_lt_succ
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next xs b c _ => show Nat.succ b > 0; apply Nat.zero_lt_succ
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next => decide
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