19 lines
654 B
Text
19 lines
654 B
Text
import algebra.group
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open algebra
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constant f {A : Type} : A → A → A
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theorem test1 {A : Type} [s : add_ab_group A] (a b c : A) : f (a + 0) (f (a + 0) (a + 0)) = f a (f (0 + a) a) :=
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begin
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rewrite [
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add_zero at {1, 3}, -- rewrite 1st and 3rd occurrences
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{0 + _}add.comm] -- apply commutativity to (0 + _)
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end
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axiom Ax {A : Type} [s₁ : has_mul A] [s₂ : has_one A] (a : A) : f (a * 1) (a * 1) = 1
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theorem test2 {A : Type} [s : ab_group A] (a b c : A) : f a a = 1 :=
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begin
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rewrite [-(mul_one a), -- - means apply symmetry, rewrite 0 ==> a * 0 at 1st and 2nd occurrences
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Ax] -- use Ax as rewrite rule
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end
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