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 Th18:
  W.(a,p) = x & W.(a,b) = v implies (*'(a,p) = b iff Phi(a,x) = v)
proof
  assume that
A1: W.(a,p) = x and
A2: W.(a,b) = v;
  Phi(a,x) = W.(a,*'(a,p)) by A1,Th15;
  hence thesis by A2,MIDSP_2:32;
end;
