Can we write formal (mechanical) proof of any theorem?

Question

why formal proofs are not widely used? sometimes non formal proofs are cumbersome. are there any "important" theorems that have been proved formally

Relevant: State of the progress of automated proof checking – hmakholm left over Monica May 23 '16 at 11:42 — hmakholm left over Monica, May 23 '16 at 11:42

score 0 · Answer 1 · answered Jul 09 '17 at 14:33

Because are very difficult to write:

To write a correct and complete formal proof one must have a complete command of both maths and logic.

Then a lot of work on all fields of mathematics .

Anyway the only book as far as i know existing which is full of formal proofs is one titled:

FORMAL PROOFS IN MATHS In amazon.com

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