8 lines
362 B
Text
8 lines
362 B
Text
axiom addz {A : Type} [has_add A] [has_zero A] : ∀ a : A, a + 0 = a
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axiom addc {A : Type} [has_add A] : ∀ a b : A, a + b = b + a
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example {A : Type} [has_add A] [has_zero A] [has_one A] (a b c : A) : b = 0 → a + b + c = c + a :=
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assume h,
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calc a + b + c = a + 0 + c : by rw h
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... = a + c : by rw addz
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... = c + a : by rw addc
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