% SZS status Theorem for pair__to__num__formu
% SZS output start Proof for pair__to__num__formu
  file('i/f/pred_set/pair__to__num__formula',ah4s_predu_u_sets_pairu_u_tou_u_numu_u_def)).
  file('i/f/pred_set/pair__to__num__formula',ah4s_numpairs_triu_u_formula)).
  file('i/f/pred_set/pair__to__num__formula',ch4s_predu_u_sets_pairu_u_tou_u_numu_u_formula)).
  file('i/f/pred_set/pair__to__num__formula',ah4s_arithmetics_MULTu_u_COMM)).
  file('i/f/pred_set/pair__to__num__formula',ah4s_numpairs_npairu_u_def)).
% SZS output end Proof for pair__to__num__formu
