[fgh]

Does this include the full machinery to prove the necessary theorems or are these basically practical courses?

[zmgsabst]

Those are practical courses, meant to prep for linear algebra and differential equations — and various STEM tracks. As I recall, there were some proofs (eg, limits showing derivative rules; limits showing sums for integral rules).

We covered all the proofs in real analysis 1 (derivatives; sequences) and 2 (integrals; measure).