Question

这是我在此练习的进展：https://github.com/userhr/MIT-6.826-2017

(** **** Exercise: 2 stars (andb_true_elim2)  *)
(** Prove the following claim, marking cases (and subcases) with
    bullets when you use [destruct]. *)

Theorem andb_true_elim2 : forall b c : bool,
  andb b c = true -> c = true.
Proof.
  intros c.
  (** Prove anything && false == false. *)
  assert (forall x : bool, andb x false = false) as H.
  destruct x. 
   -reflexivity.
   -reflexivity.
   (** Obviously true at this point since we have shown that no 
       matter what, andb b c will be false if one of them is 
       false. My idea is to use H to show that if it is to be 
       true, than both arguments must be true.
   *)
Qed.

我之所以有必要表明(forall x : bool, andb x false = false)是因为我无法通过证明(forall a b : bool, andb a b = true -> a = true, b = true)

来证明如何做出明显的证据

Answer 1

我已经在https://github.com/hckkid/sfsol

托管了大多数软件基础问题的解决方案

至于这个特定的练习，请参考https://github.com/hckkid/sfsol/blob/master/Chap1.v#L385

自从我解决了软件基础以来，章节发生了变化。

此代码段是

Theorem andb_true_elim2 : forall b c : bool,
  andb b c = true -> c = true.
Proof.
  intros b c H.
  destruct c.
  Case "c = true".
    reflexivity.
  Case "c = false".
    rewrite <- H.
  destruct b.
  SCase "b = true".
    reflexivity.
  SCase "b = false".
    reflexivity.
Qed.

如何完成涉及布尔值的这个简单证明

1 个答案: