49 lines
1.1 KiB
Text
49 lines
1.1 KiB
Text
def ex1 (p : Prop) (h1 : p) (h2 : p → False) : α := by
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contradiction
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def ex2 (p : Prop) (h1 : p) (h2 : ¬ p) : α := by
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contradiction
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def ex3 (p : Prop) (h1 : id p) (h2 : ¬ p) : α := by
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contradiction
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def ex4 (p : Prop) (h1 : id p) (h2 : id (Not p)) : α := by
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contradiction
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def ex5 (h : x+1 = 0) : α := by
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contradiction
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def ex6 (h : 0+0 ≠ 0) : α := by
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contradiction
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def ex7 (x : α) (h : Not (x = x)) : α := by
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contradiction
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def ex8 (h : 0+0 = 0 → False) : α := by
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contradiction
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def ex9 (h : 10 = 20) : α := by
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contradiction
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def ex10 (h : [] = [1, 2, 3]) : α := by
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contradiction
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def ex11 (h : id [] = [1, 2, 3]) : α := by
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contradiction
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def ex12 (h : False) : α := by
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contradiction
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def ex13 (h : id False) : α := by
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contradiction
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def ex14 (h : 100000000 ≤ 20) : α := by
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contradiction
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def ex15 (x : α) (h : x = x → False) : α := by
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contradiction
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theorem ex16 (xs : List α) (h : xs = [] → False) : Nonempty α := by
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cases xs using List.rec with
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| nil => contradiction
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| cons x _ => apply Nonempty.intro; assumption
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