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 Th14:
  (for m holds x.m = y.m) implies x = y
proof
  assume
A1: for m holds x.m = y.m;
  for j be Nat st j in Seg(n+1) holds x.j = y.j
  proof
    let j be Nat;
    assume j in Seg(n+1);
    then reconsider j as Nat of n by Th7;
    x.j = y.j by A1;
    hence thesis;
  end;
  hence thesis by FINSEQ_2:119;
end;
