No. A postulate need not be true.
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logic postulates theorems
the theorems and postulates used in the proof
No, because postulates are assumptions. Some true, some not. Proving a Theorem requires facts in a logical order to do so.
Postulates are statements that are assumed to be true without proof. Theorums are statements that can be deduced and proved from definitions, postulates, and previously proved theorums.
A proof uses postulates and theorems to prove some statement.