How to write a formal proof of Euclid’s Theorem, specifying every logic rule used?


How do you write a formal proof?

Write out the beginning very carefully. Write down the definitions very explicitly, write down the things you are allowed to assume, and write it all down in careful mathematical language. Write out the end very carefully. That is, write down the thing you’re trying to prove, in careful mathematical language.

What is a formal proof in logic?

A formal proof is a proof in which every logical inference has been checked all the way back to the fundamental axioms of mathematics. All the intermediate logical steps are supplied, without exception.

How to prove a theorem?

In order for a theorem be proved, it must be in principle expressible as a precise, formal statement. However, theorems are usually expressed in natural language rather than in a completely symbolic form—with the presumption that a formal statement can be derived from the informal one.

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