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;
reserve RAS for ReperAlgebra of n;
reserve a,b,pm,p9m,p99m for Point of RAS;
reserve p for Tuple of (n+1),RAS;
reserve W for ATLAS of RAS;
reserve v for Vector of W;
reserve x for Tuple of (n+1),W;

theorem Th23:
  W.(a,p) = x & W.(a,b) = v & Phi(x) = v implies *'(a,p) = b
proof
  assume
A1: W.(a,p) = x & W.(a,b) = v & Phi(x) = v;
  Phi(x) = Phi(a,x) by Def12;
  hence thesis by A1,Th18;
end;
