let a, b, c, d be Real; ( a <= b & c <= d implies SW-corner (rectangle (a,b,c,d)) = |[a,c]| )
set K = rectangle (a,b,c,d);
assume that
A1:
a <= b
and
A2:
c <= d
; SW-corner (rectangle (a,b,c,d)) = |[a,c]|
A3:
SW-corner (rectangle (a,b,c,d)) = |[(W-bound (rectangle (a,b,c,d))),(S-bound (rectangle (a,b,c,d)))]|
by PSCOMP_1:def 11;
W-bound (rectangle (a,b,c,d)) = a
by A1, A2, Th36;
hence
SW-corner (rectangle (a,b,c,d)) = |[a,c]|
by A1, A2, A3, Th39; verum