theorem Th48:
  r1*(i|->r2) = i|->(r1*r2)
proof
  reconsider s1=r1, s2=r2 as Element of REAL by XREAL_0:def 1;
  s1*(i|->s2) = i|->((multreal[;](s1,id REAL)).s2) by FINSEQOP:16
    .= i|->(r1*r2) by Lm1;
  hence thesis;
end;
