引入先前证明的定理作为假设

假设我已经在coq中证明了某个定理，稍后我想将其作为假设引入到另一个定理的证明中。有没有一种简洁的方法来做到这一点？

当我想做一些诸如案例证明之类的事情时，我通常会出现这种需要。我发现做到这一点的一种方法是assert陈述定理，然后立即证明它，但这似乎有点麻烦。例如，我倾向于写这样的东西：

Require Import Arith.EqNat.

Definition Decide P := P \/ ~P.

Theorem decide_eq_nat: forall x y: nat, Decide (x = y).
Proof.
  intros x y. remember (beq_nat x y) as b eqn:E. destruct b.
    left. apply beq_nat_eq. assumption.
    right. apply beq_nat_false. symmetry. assumption. Qed.

Theorem silly: forall x y: nat, x = y \/ x <> y.
Proof.
  intros x y.
  assert (Decide (x = y)) as [E|N] by apply decide_eq_nat.
    left. assumption.
    right. assumption. Qed.

但是有没有比输入整个内容更简单的方法呢？assert [statement] by apply [theorem] thing?

您可以使用pose proof theorem_name as X., where X是您要介绍的名字。

如果您要立即销毁它，您还可以：destruct (decide_eq_nat x y).