reserve m,n for Nat;
reserve i,j for Integer;
reserve S for non empty addMagma;
reserve r,r1,r2,s,s1,s2,t,t1,t2 for Element of S;
reserve G for addGroup-like non empty addMagma;
reserve e,h for Element of G;
reserve G for addGroup;
reserve f,g,h for Element of G;
reserve u for UnOp of G;
reserve A for Abelian addGroup;
reserve a,b for Element of A;

theorem
  for L be add-unital non empty addMagma for x be Element of L holds (mult
  L).(2,x) = x+x
proof
  let L be add-unital non empty addMagma;
  let x be Element of L;
  1+1 = 2;
  hence (mult L).(2,x) = (mult L).(1,x) + x by Def7
    .= x + x by Th49;
end;
