reserve E for RealLinearSpace;
reserve A, B, C for binary-image of E;
reserve a, b, v for Element of E;
reserve F, G for binary-image-family of E;
reserve A, B, C for non empty binary-image of E;

theorem Th22:
  A c= B implies A(-)C c= B(-)C
  proof
    assume
    A1: A c= B;
    let x be object;
    assume x in A(-)C;
    then consider w be Element of E such that
    A2: x = w & for c be Element of E st c in C holds w - c in A;
    for c being Element of E st c in C holds w - c in B by A1,A2;
    hence x in B(-)C by A2;
  end;
