被 xcc 忽略去做了一小时 必须写出来 不然亏了.jpg

Let be a Set satisfy that or there exists an element y .

Let + be a operator that _+_ =_ take 2 elements in as arguments and return another element in staisfy that

prove: a+b = b+a.

Lemma 1.

Proof:

firstly if because

let a be we'll get

secondly if for , , let's prove

by mathematical induction we prove .

Lemma 2.

Proof:

firstly if since

secondly if for , , let's prove .

Lemma 3.

Proof:

firstly if since

secondly if for , , let's prove .

Proposition 1.

Proof:

firstly if since Lemma 1. the proposition is true

secondly if for , , let's prove that .

Q. E. D.