23 lines
923 B
Text
23 lines
923 B
Text
set_option pp.rawOnError true
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theorem ex1 (f : Nat → Nat) (x : Nat) (h1 : (x : Nat) → x > 0 → f x = x) (h2 : x > 0) : f x = x := by
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exact h1 _ _
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theorem ex2 (f : Nat → Nat) (x : Nat) (h1 : (x : Nat) → x > 0 → f x = x) (h2 : x > 0) : f x = x := by
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refine h1 _ _
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theorem ex3 (f : Nat → Nat) (x : Nat) (h1 : (x : Nat) → x > 0 → f x = x) (h2 : x > 0) : f x = x := by
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first | exact h1 _ _ | apply h1
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assumption
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theorem ex4 (f : Nat → Nat) (x : Nat) (h1 : (x : Nat) → x > 0 → f x = x) (h2 : x > 0) : f x = x := by
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first | refine h1 _ _ | apply h1
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assumption
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theorem ex5 (f g : Nat → Nat) (x : Nat) (h1 : (x : Nat) → x > 0 → f x = x) (h2 : x > 0) (h3 : g x = x) : f x = x := by
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first | apply h3 | apply h1
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assumption
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theorem ex6 (f : Nat → Nat) (x : Nat) (h1 : (x : Nat) → x > 0 → f x = x) (h2 : x > 0) : f x = x := by
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first | refine h1 _ _ | refine h1 _ _
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assumption
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