let a, b, c, d be ext-real number ; :: thesis: ( a <= b & c <= d implies max a,c <= max b,d )
assume that
A1: a <= b and
A2: c <= d ; :: thesis: max a,c <= max b,d
d <= max b,d by Th25;
then A3: c <= max b,d by A2, Th2;
b <= max b,d by Th25;
then a <= max b,d by A1, Th2;
hence max a,c <= max b,d by A3, Def10; :: thesis: verum