let a, b, c, d be ExtReal; :: 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, Def8; :: thesis: verum