Cheng Yi's system rests on a pair of terms. Li is pattern or principle, the way a thing ought to be and the reason it is as it is; qi is the psychophysical stuff that any actual thing is made of. Everything that exists has both. The li of a thing is perfect and is continuous with the li of everything else, so that in his formula there is one principle with many particularisations. Qi is what varies in clarity and density, and it is where imperfection, obstruction and bad character come from.
From this he draws the claim that made his branch of the school distinctive: the nature is principle. Human nature as such is good without qualification, and what is actually observed in a person is nature refracted through their endowment of qi. Moral cultivation is therefore not the manufacture of virtue but the clearing of an obstruction.
The practice has two halves and he insisted on both. One is the investigation of things, a phrase from the Great Learning that he read as patient and repeated study of particular matters, texts, affairs, natural things, until the pattern common to them is grasped; he explicitly denied that one could exhaust all things and said that sustained work on many eventually opens out. The other is abiding in reverence, a settled inward composure maintained in ordinary activity rather than in withdrawal.
His brother Cheng Hao had emphasised the direct apprehension of unity with all things. Cheng Yi's slower, more analytic route is the one Zhu Xi took up, and it is the reason the resulting orthodoxy is named for the two of them.