"A promise made easily will be broken" corresponds to three famous sayings: "Be quiet when you make a promise", "Don't break your word" and "a small letter will become a big letter".

"Make a promise lightly and be taciturn" comes from Chapter 63 of Laozi, which means that promises made easily are bound to lack credibility.

"Break your word without standing" comes from Zuo Zhuan's Twenty-two Years of "xianggong", which means that people who break their word are untenable in society. It means that you can't stand on the society and be recognized by others.

"A small letter leads to a big letter" comes from "Han Feizi's foreign storage", which means that a small letter can be established before a big letter can be established.