reserve q,r,c,c1,c2,c3 for Quaternion;
reserve x1,x2,x3,x4,y1,y2,y3,y4 for Real;

theorem Th3:
  c + 0q = c
proof
A1: 0q =[*In(0,REAL),In(0,REAL)*] by ARYTM_0:def 5
    .=[*0,0,0,0*] by QUATERNI:91;
  consider x,y,w,z be Element of REAL such that
A2: c = [*x,y,w,z*] by Lm1;
  c + 0q = [* x+0,y+0,w+0,z+0 *] by A1,A2,QUATERNI:def 7
    .= [*x,y,w,z*];
  hence thesis by A2;
end;
