let a, b, c, d be real number ; :: thesis: ( 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 ; :: thesis: 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 37;
E-bound (rectangle (a,b,c,d)) = b by A1, A2, Th48;
hence SE-corner (rectangle (a,b,c,d)) = |[b,c]| by A1, A2, A3, Th49; :: thesis: verum