let S1, S2, T1, T2 be complete LATTICE; ( S1,S2 are_isomorphic & T1,T2 are_isomorphic implies UPS (S2,T1), UPS (S1,T2) are_isomorphic )
given f being Function of S1,S2 such that A1:
f is isomorphic
; WAYBEL_1:def 8 ( not T1,T2 are_isomorphic or UPS (S2,T1), UPS (S1,T2) are_isomorphic )
given g being Function of T1,T2 such that A2:
g is isomorphic
; WAYBEL_1:def 8 UPS (S2,T1), UPS (S1,T2) are_isomorphic
take
UPS (f,g)
; WAYBEL_1:def 8 UPS (f,g) is isomorphic
thus
UPS (f,g) is isomorphic
by A1, A2, Th35; verum