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- Section Group.
- Variable A: Type.
- Variable op: A -> A -> A.
- Definition is_left_neutral (e: A) := forall x: A, (op e x) = x.
- Definition is_right_neutral (e: A) := forall x: A, x = (op x e).
- Lemma uniqueness_of_neutral:
- forall a b: A, (is_left_neutral a) -> (is_right_neutral b) -> (a = b).
- Proof.
- intro; intro.
- intros lna rnb.
- elim lna with b; elim rnb with a.
- reflexivity.
- Qed.
- End Group.
- Definition is_left_neutral (e: A) := forall x: A, x = (op e x).
- Definition is_right_neutral (e: A) := forall x: A, (op x e) = x.
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