let a, b, c, d be real number ; :: thesis: ( 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 ; :: thesis: 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 34;
W-bound (rectangle a,b,c,d) = a by A1, A2, Th46;
hence SW-corner (rectangle a,b,c,d) = |[a,c]| by A1, A2, A3, Th49; :: thesis: verum