A postulate is something we assume to be true. We usually use postulates to prove theorems.
Theorem: A proposition that has been or is to be proved on the basis of explicit assumptions.
Corollary: A proposition that follows with little or no proof required from one already proven.
Theorems give rise to corollaries. Usually a corollary is very easy to prove using the theorem that it arose from.
I used this dictionary for some formal definitions:
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