45 lines
933 B
Text
45 lines
933 B
Text
import algebra.ring data.nat
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open algebra
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variables {A : Type}
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section
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variables [s : add_comm_monoid A]
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include s
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attribute add.comm [forward]
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attribute add.assoc [forward]
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set_option blast.simp false
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set_option blast.subst false
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set_option blast.ematch true
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theorem add_comm_three (a b c : A) : a + b + c = c + b + a :=
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by blast
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theorem add.comm4 : ∀ (n m k l : A), n + m + (k + l) = n + k + (m + l) :=
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by blast
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end
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section
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variable [s : group A]
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include s
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attribute mul.assoc [forward]
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attribute mul.left_inv [forward]
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attribute one_mul [forward]
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set_option blast.simp false
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set_option blast.subst false
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set_option blast.ematch true
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theorem inv_mul_cancel_left (a b : A) : a⁻¹ * (a * b) = b :=
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by blast
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attribute mul_one [forward]
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attribute inv_mul_cancel_right [forward]
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-- TODO(Leo): check if qfc can get this one
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-- theorem inv_eq_of_mul_eq_one {a b : A} (H : a * b = 1) : a⁻¹ = b :=
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-- by blast
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end
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