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 Th30:
  for X holds Y = {p: ex f st f is_a_proof_wrt X & Effect(f) = p}
  implies Y is being_a_theory
by Lm3,Lm4,Lm5,Lm6,Lm7,Lm8,Lm9,Lm10,Lm11;
