 reserve i,j,n,k,l for Nat;
 reserve T,S,X,Y,Z for Subset of MC-wff;
 reserve p,q,r,t,F,H,G for Element of MC-wff;
 reserve s,U,V for MC-formula;
reserve f,g for FinSequence of [:MC-wff,Proof_Step_Kinds_IPC:];

theorem Th14:
  for X holds Y = {p: ex f st f is_a_proof_wrt_IPC X & Effect_IPC(f) = p}
  implies Y is IPC_theory by Lm2,Lm3,Lm4,Lm5,Lm6,Lm7,Lm8,Lm9,Lm10,Lm11;
