theorem Th35:
  x = Class(EqRel(S),a) & y = Class(EqRel(S),b) implies
    x+y = Class(EqRel(S),a+b)
   proof
     consider a1, b1 being Element of Frac(S) such that
A1:  x = Class(EqRel(S),a1) & y = Class(EqRel(S),b1) and
A2:  (the addF of S~R).(x,y) = Class(EqRel(S),a1+b1) by Def6;
     assume x = Class(EqRel(S),a) & y = Class(EqRel(S),b); then
     a,a1 Fr_Eq S & b,b1 Fr_Eq S by A1,Th26;
     hence thesis by A2,Th26,Th28;
   end;
