theorem
  (a1 + a2)*R = a1*R + a2*R
proof
  thus (a1 + a2)*R = (the addF of K).:((the multF of K)[;](a1,id the carrier
  of K), (the multF of K)[;](a2,id the carrier of K))*R by Th10,FINSEQOP:35
    .= a1*R + a2*R by FUNCOP_1:25;
end;
