19 lines
494 B
Text
19 lines
494 B
Text
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import algebra.ring
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open algebra eq.ops
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variable {A : Type}
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theorem zero_mul1 [s : ring A] (a : A) : 0 * a = 0 :=
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have H : 0 * a + 0 = 0 * a + 0 * a,
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begin
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rewrite add_zero,
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rewrite -(add_zero 0) at {1},
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rewrite right_distrib
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end,
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show 0 * a = 0, from (add.left_cancel H)⁻¹
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theorem zero_mul2 [s : ring A] (a : A) : 0 * a = 0 :=
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have H : 0 * a + 0 = 0 * a + 0 * a,
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by rewrite [add_zero, -(add_zero 0) at {1}, right_distrib],
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show 0 * a = 0, from (add.left_cancel H)⁻¹
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