[proof] ITE translation fix (#3484)

[proof] ITE translation fix (#3484)

* Bugfix: convert ifte arms to formulas for printing

We have two kinds of ITEs in our LFSC proofs:
   * ite: for sort-typed expressions
   * ifte: for formulas
Say that we have a Bool-sorted ITE. We had machinery for emitting an
`ifte` for it, but this machinery didn't actually convert the arms of
the ITE into formulas... Facepalm.

Fixed now.

* Test the lifting of ITEs from arithmetic.

This test verifies that booleans ITEs are correctly lifted to formula
ITEs in LRA proofs.

It used to fail, but now passes.

* clang-format

* Typos.

* Add test to CMake

* Set --check-proofs in test

* Address Yoni

* Expand printsAsBool documentation
* Assert ITE typing soundness

* Assert a subtype relation for ITEs, not equality

* Update src/proof/arith_proof.h

Thanks Yoni!

Co-Authored-By: yoni206 <yoni206@users.noreply.github.com>
Co-authored-by: yoni206 <yoni206@users.noreply.github.com>