reserve Al for QC-alphabet;
reserve i,j,n,k,l for Nat;
reserve a for set;
reserve T,S,X,Y for Subset of CQC-WFF(Al);
reserve p,q,r,t,F,H,G for Element of CQC-WFF(Al);
reserve s for QC-formula of Al;
reserve x,y for bound_QC-variable of Al;
reserve f,g for FinSequence of [:CQC-WFF(Al),Proof_Step_Kinds:];

theorem Th19:
  for n being Nat holds 1 <= n & n <= len f implies
  (f.n)`2 = 0 or ... or (f.n)`2 = 9
proof
  let n be Nat;
  assume
A1: 1 <= n & n <= len f;
 dom f = Seg len f by FINSEQ_1:def 3;
then  n in dom f by A1,FINSEQ_1:1;
  then
 rng f c= [:CQC-WFF(Al),Proof_Step_Kinds:] & f.n in rng f by FINSEQ_1:def 4
,FUNCT_1:def 3;
then  (f.n)`2 in Proof_Step_Kinds by MCART_1:10;
then  ex k st k = (f.n)`2 & k <= 9;
  hence thesis;
end;
