let a, b, c, d be ext-real number ; :: thesis: ( a <= b & c <= d implies min a,c <= min b,d )
assume that
A1: a <= b and
A2: c <= d ; :: thesis: min a,c <= min b,d
min a,c <= c by Th17;
then A3: min a,c <= d by A2, Th2;
min a,c <= a by Th17;
then min a,c <= b by A1, Th2;
hence min a,c <= min b,d by A3, Def9; :: thesis: verum