% SZS status Theorem for pair__to__num__inv_
% SZS output start Proof for pair__to__num__inv_
  file('i/f/pred_set/pair__to__num__inv_c0',ch4s_predu_u_sets_pairu_u_tou_u_numu_u_invu_c0)).
  file('i/f/pred_set/pair__to__num__inv_c0',ah4s_numpairs_npair0)).
  file('i/f/pred_set/pair__to__num__inv_c0',ah4s_predu_u_sets_numu_u_tou_u_pairu_u_def)).
  file('i/f/pred_set/pair__to__num__inv_c0',ah4s_predu_u_sets_pairu_u_tou_u_numu_u_def)).
% SZS output end Proof for pair__to__num__inv_
