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;
