Definition hfsqstrtocommsqstr {X X' Y Z : UU} (f : X -> Y) (f' : X' -> Y) (g : Z -> X) (g' : Z -> X') : hfsqstr f f' g g' -> commsqstr g' f' g f := @pr1 _ (λ h : commsqstr g' f' g f, isweq (commsqZtohfp f f' g g' h)).