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 Th14:
  1 in dom <*c,d*> & 2 in dom <*c,d*> &
  (f^<*c,d*>).(len f + 1) = c & (f^<*c,d*>).(len f + 2) = d
proof
A1: 2 <= len <*c,d*> by FINSEQ_1:44;
  then 2 in dom <*c,d*> by FINSEQ_3:25;
  then
A2: (f^<*c,d*>).(len f+2) = <*c,d*>.2 by FINSEQ_1:def 7;
  1 <= 2;
  then
A3: 1 <= len <*c,d*> by FINSEQ_1:44;
  then 1 in dom <*c,d*> by FINSEQ_3:25;
  then (f^<*c,d*>).(len f+1) = <*c,d*>.1 by FINSEQ_1:def 7;
  hence thesis by A3,A1,A2,FINSEQ_3:25;
end;
