
theorem sa:
for X being non empty set
for R being Ring
for L being scalar-associative non empty ModuleStr over R
for a,b being Element of R
for f being Function of X,L holds (a * b) '*' f = a '*' (b '*' f)
proof
let X be non empty set, F be Ring,
    L be scalar-associative non empty ModuleStr over F,
    a,b be Element of F, f be Function of X,L;
now let o be object;
  assume o in X;
  then reconsider x = o as Element of X;
  thus ((a * b) '*' f).o
     = (a * b) * (f.x) by defmu
    .= a * (b * f.x) by VECTSP_1:def 16
    .= a * (b '*' f).x by defmu
    .= (a '*' (b '*' f)).o by defmu;
  end;
hence thesis by FUNCT_2:12;
end;
