reserve A for non empty closed_interval Subset of REAL;

theorem Lmbcd:
  for b,c,d be Real st b > 0 & c > 0 & d > 0 holds
    (b-d)/(b/c) < c
proof
  let b,c,d be Real;
  assume
  A1:b > 0 & c > 0 & d > 0; then
  -d+b < 0+b by XREAL_1:8; then
  (b-d)/b < b/b by A1,XREAL_1:74; then
  ((b-d)/b) < 1 by A1,XCMPLX_1:60; then
  ((b-d)/b)*c < 1*c by A1,XREAL_1:68;
  hence thesis by XCMPLX_1:82;
end;
