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Axiom A : Set. Axiom A_eq_dec: forall a b: A, { a = b } + { a <> b }. Axiom A_mul : A -> A -> A. Axiom A_zero: A. Axiom A_one: A. Infix "*" := A_mul. Notation "0" := A_zero. Notation "1" := A_one. Axiom A_mul_assoc: forall a b c, (a * b) * c = a * (b * c). Axiom A_mul_comm: forall a b, a * b = b * a. Axiom A_mul_1_r: forall a, a * 1 = a. Axiom A_mul_inv_ex: forall a, a <> 0 -> { a': A | a * a' = 1 }. Axiom A_mul_0_r: forall a, a * 0 = 0.
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