reserve a,b,c,d,x,y,w,z,x1,x2,x3,x4 , X for set;
reserve A for non empty set;
reserve i,j,k for Element of NAT;
reserve a,b,c,d for Real;
reserve y,r,s,x,t,w for Element of RAT+;
reserve z,z1,z2,z3,z4 for Quaternion;

theorem
  Rea (1q) = 1 & Im1(1q) = 0 & Im2 (1q) = 0 & Im3 (1q) = 0
 by Lm10,Th16;
