24 lines
860 B
Text
24 lines
860 B
Text
theorem ex1 (x : Nat) : 0 + x = x := by
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cases x with
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| zero => skip -- Error: unsolved goals
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| succ y => skip -- Error: unsolved goals
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theorem ex2 (x : Nat) : 0 + x = x := by
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induction x with
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| zero => skip -- Error: unsolved goals
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| succ y ih => skip -- Error: unsolved goals
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theorem ex3 (x : Nat) : 0 + x = x := by
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cases x with
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| zero => rfl
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| succ y => skip -- Error: unsolved goals
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theorem ex4 (x : Nat) {y : Nat} (h : y > 0) : x % y < y := by
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induction x, y using Nat.mod.inductionOn generalizing h with
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| ind x y h₁ ih => skip -- Error: unsolved goals
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| base x y h₁ => skip -- Error: unsolved goals
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theorem ex5 (x : Nat) {y : Nat} (h : y > 0) : x % y < y := by
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cases x, y using Nat.mod.inductionOn with
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| ind x y h₁ ih => skip -- Error: unsolved goals
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| base x y h₁ => skip -- Error: unsolved goals
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