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 Th28:
  f is_a_proof_wrt X implies Effect(f) in Cn(X)
proof
  assume
A1: f is_a_proof_wrt X;
then A2: 1 <= len f by Th21;
then A3: (f.(len f))`1 in Cn(X) by A1,Th27;
 f <> {} by A2;
  hence thesis by A3,Def6;
end;
