Finiteness assumption in explorable media

Explorable and interactive media seem to bake in an assumption of finiteness, which makes it challenging to interact with the infinite and arbitrary objects that appear in mathematics.

Examples:

• the explorables in https://explorabl.es/math/
• The Witness builds up complex puzzles starting from simple ones. But each puzzle is finite (finite board size, finite state space)

The kind of explorable medium that I'm interested in would somehow encode the proof-writing/proof-generating process so the user can do real math. But how do you prove things about e.g. an arbitrary compact metric space? How would you "explore" something that requires a proof by contradiction (which would require representing impossible situations)?