alias nat          /Coq/Init/Datatypes/nat.ind#1/1
alias eqT          /Coq/Init/Logic_Type/eqT.ind#1/1
alias eq           /Coq/Init/Logic/eq.ind#1/1
alias refl_equal   /Coq/Init/Logic/eq.ind#1/1/1
alias eq_ind       /Coq/Init/Logic/eq_ind.con
alias eq_ind_r     /Coq/Init/Logic/eq_ind_r.con
alias O            /Coq/Init/Datatypes/nat.ind#1/1/1
alias S            /Coq/Init/Datatypes/nat.ind#1/1/2
alias plus         /Coq/Init/Peano/plus.con
alias mult         /Coq/Init/Peano/mult.con
alias le           /Coq/Init/Peano/le.ind#1/1
alias lt           /Coq/Init/Peano/lt.con
alias not          /Coq/Init/Logic/not.con
alias f_equal      /Coq/Init/Logic/f_equal.con
alias le_trans     /Coq/Arith/Le/le_trans.con

alias plus_n_O     /Coq/Init/Peano/plus_n_O.con 

alias or           /Coq/Init/Logic/or.ind#1/1
alias or_ind       /Coq/Init/Logic/or_ind.con

(or (eq nat O O) (eq nat O O)) -> (lt O O)