reserve n,i,j,k,l for Nat;
reserve D for non empty set;
reserve c,d for Element of D;
reserve p,q,q9,r for FinSequence of D;
reserve RAS for MidSp-like non empty ReperAlgebraStr over n+2;
reserve a,b,d,pii,p9i for Point of RAS;
reserve p,q for Tuple of (n+1),RAS;
reserve m for Nat of n;
reserve W for ATLAS of RAS;
reserve v for Vector of W;
reserve x,y for Tuple of (n+1),W;

theorem
  i in Seg(n+1) implies (x+*(i,v)).i = v & for l st l in (dom x)\{i}
  holds (x+*(i,v)).l = x.l by Lm1,Lm2;
