The best replacement for postulate is axiom.

The best alternatives to postulate are rated as following:
★★★★★  axiom
★★★  theorem
★★  posit
★  theorem geometry
★  conjecture
★  axion
★  hypothesis

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Speaking about postulate, one probably shouldn't forget about proof.

Other search terms related to postulate and their ratings are:
★★★★★ proof
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