reserve R,R1 for commutative Ring;
reserve A,B for non degenerated commutative Ring;
reserve o,o1,o2 for object;
reserve r,r1,r2 for Element of R;
reserve a,a1,a2,b,b1 for Element of A;
reserve f for Function of R, R1;
reserve p for Element of Spectrum A;
reserve S for non empty multiplicatively-closed Subset of R;
reserve u,v,w,x,y,z for Element of Frac(S);
reserve a, b, c for Element of Frac(S);
reserve x, y, z for Element of S~R;
reserve S for without_zero non empty multiplicatively-closed Subset of A;

theorem Lm49:
   for a,b being Element of A holds
   (canHom(S)).(a-b) = (canHom(S)).a - (canHom(S)).b
   proof
     let a,b be Element of A;
     thus
     (canHom(S)).(a-b) = (canHom(S)).a + (canHom(S)).(-b) by VECTSP_1:def 20
     .= (canHom(S)).a - (canHom(S)).b by RING_2:7;
   end;
