let a, b, c, d be Real; ( a <= b & c <= d implies SE-corner (rectangle (a,b,c,d)) = |[b,c]| )
set K = rectangle (a,b,c,d);
assume that
A1:
a <= b
and
A2:
c <= d
; SE-corner (rectangle (a,b,c,d)) = |[b,c]|
A3:
SE-corner (rectangle (a,b,c,d)) = |[(E-bound (rectangle (a,b,c,d))),(S-bound (rectangle (a,b,c,d)))]|
by PSCOMP_1:def 14;
E-bound (rectangle (a,b,c,d)) = b
by A1, A2, Th38;
hence
SE-corner (rectangle (a,b,c,d)) = |[b,c]|
by A1, A2, A3, Th39; verum