MATH.2:4.5 - Check which answers can be recovered and use the result

A value q(a) can be recovered from [a] when it is constant on that class: a~b ⇒ q(a)=q(b). Then define q_bar([a])=q(a). If this fails, return to the original objects, retain more information, or return the range of possibilities when that answers the question.

Use the quotient for the declared operations and answers. A new operation or query can require a finer relation. The old quotient retains its earlier use; revise the part that the new question distinguishes.

Stop with a valid class-level operation and usable answer, or with a counterexample identifying the lost operation or quantity. Additional formalization is useful only when it resolves a remaining mathematical or receiving question.