Definition induced_function3 : quotient R -> quotient S -> quotient T :=
induced_function2arg projf2 equivR equivS projf2_well_defined.

Lemma induced_function3_correct: forall (a:A) (b:B),
induced_function3 (quotient_projection R a)
(quotient_projection S b) =
quotient_projection T (f a b).