reserve G for non empty addLoopStr;
reserve x for Element of G;
reserve M for non empty MidStr;
reserve p,q,r for Point of M;
reserve w for Function of [:the carrier of M,the carrier of M:], the carrier
  of G;
reserve S for non empty set;
reserve a,b,b9,c,c9,d for Element of S;
reserve w for Function of [:S,S:],the carrier of G;
reserve G for add-associative right_zeroed right_complementable non empty
  addLoopStr;
reserve x for Element of G;
reserve w for Function of [:S,S:],the carrier of G;
reserve G for add-associative right_zeroed right_complementable Abelian non
  empty addLoopStr;
reserve x for Element of G;
reserve w for Function of [:S,S:],the carrier of G;
reserve M for MidSp;
reserve p,q,r,s for Point of M;
reserve G for midpoint_operator add-associative right_zeroed
  right_complementable Abelian non empty addLoopStr;
reserve x,y for Element of G;
reserve x,y for Element of vectgroup(M);

theorem Th23:
  p@q = r iff vect(p,r) = vect(r,q)
proof
  p@q = r iff p@q = r@r by MIDSP_1:def 3;
  hence thesis by Th22;
end;
