let a, b, r, s be real number ; ( a <= b & r <= s implies [:(Closed-Interval-TSpace a,b),(Closed-Interval-TSpace r,s):], Trectangle a,b,r,s are_homeomorphic )
set C1 = Closed-Interval-TSpace a,b;
set C2 = Closed-Interval-TSpace r,s;
assume A1:
( a <= b & r <= s )
; [:(Closed-Interval-TSpace a,b),(Closed-Interval-TSpace r,s):], Trectangle a,b,r,s are_homeomorphic
then reconsider h = R2Homeomorphism | the carrier of [:(Closed-Interval-TSpace a,b),(Closed-Interval-TSpace r,s):] as Function of [:(Closed-Interval-TSpace a,b),(Closed-Interval-TSpace r,s):],(Trectangle a,b,r,s) by Th57;
take
h
; T_0TOPSP:def 1 h is being_homeomorphism
thus
h is being_homeomorphism
by A1, Th58; verum