let a, b, c, d be Real; ( a <= b & c <= d implies NW-corner (rectangle (a,b,c,d)) = |[a,d]| )
assume that
A1:
a <= b
and
A2:
c <= d
; NW-corner (rectangle (a,b,c,d)) = |[a,d]|
set K = rectangle (a,b,c,d);
A3:
NW-corner (rectangle (a,b,c,d)) = |[(W-bound (rectangle (a,b,c,d))),(N-bound (rectangle (a,b,c,d)))]|
by PSCOMP_1:def 12;
W-bound (rectangle (a,b,c,d)) = a
by A1, A2, Th36;
hence
NW-corner (rectangle (a,b,c,d)) = |[a,d]|
by A1, A2, A3, Th37; verum