reserve Al for QC-alphabet;
reserve a,b,c,d for object,
  i,j,k,m,n for Nat,
  p,q,r for Element of CQC-WFF(Al),
  x,y,y0 for bound_QC-variable of Al,
  X for Subset of CQC-WFF(Al),
  A for non empty set,
  J for interpretation of Al,A,
  v,w for Element of Valuations_in(Al,A),
  Sub for CQC_Substitution of Al,
  f,f1,g,h,h1 for FinSequence of CQC-WFF(Al);
reserve fin,fin1 for FinSequence;

theorem Th12:
  0 < m implies dom (Sgm (Seg n \/ {n+m})) = Seg (n+1)
proof
  assume 0 < m;
  then len (Sgm (Seg n \/ {n+m})) = n+1 by Th11;
  hence thesis by FINSEQ_1:def 3;
end;
