let a, b, c, d be real number ; :: thesis: ( a <= b & c < d implies a - d < b - c )
assume ( a <= b & c < d ) ; :: thesis: a - d < b - c
then c - b < d - a by Th16;
then - (d - a) < - (c - b) by Lm15;
hence a - d < b - c ; :: thesis: verum