let a, b, c, d be Real; :: thesis: ( a <= b & c <= d implies a - d <= b - c )
assume that
A1: a <= b and
A2: c <= d ; :: thesis: a - d <= b - c
- d <= - c by A2, Lm14;
then a + (- d) <= b + (- c) by A1, Lm6;
hence a - d <= b - c ; :: thesis: verum