%   ORIGINAL: 'h4/thm/numpair/nlist_ind_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !P. P 'h4/const/num/0' /\ (!h t. P t ==> P ('h4/const/numpair/ncons' h t)) ==> (!n. P n)
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !P. happ P 'h4/const/num/0' /\ (!h t. happ P t ==> happ P ('h4/const/numpair/ncons' h t)) ==> (!n. happ P n)
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f63036,V_3f63032]: ![F, G]: (![X]: s(V_3f63032,happ(s(fun(V_3f63036,V_3f63032),F),s(V_3f63036,X))) = s(V_3f63032,happ(s(fun(V_3f63036,V_3f63032),G),s(V_3f63036,X))) => s(fun(V_3f63036,V_3f63032),F) = s(fun(V_3f63036,V_3f63032),G))).
fof('h4/thm/numpair/nlist_ind_', conjecture, ![P]: ((p(s(bool,happ(s(fun('h4/type/num/num',bool),P),s('h4/type/num/num','h4/const/num/0')))) & ![H, T]: (p(s(bool,happ(s(fun('h4/type/num/num',bool),P),s('h4/type/num/num',T)))) => p(s(bool,happ(s(fun('h4/type/num/num',bool),P),s('h4/type/num/num','h4/const/numpair/ncons'(s('h4/type/num/num',H),s('h4/type/num/num',T)))))))) => ![N]: p(s(bool,happ(s(fun('h4/type/num/num',bool),P),s('h4/type/num/num',N)))))).
