%   ORIGINAL: 'h4/thm/numpair/nlistrec_thm_e1'
% 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: !t n h f. 'h4/const/numpair/nlistrec' n f ('h4/const/numpair/ncons' h t) = f h t ('h4/const/numpair/nlistrec' n f t)
%   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: !t n h f. 'h4/const/numpair/nlistrec' n f ('h4/const/numpair/ncons' h t) = happ (happ (happ f h) t) ('h4/const/numpair/nlistrec' n f t)
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_3f63011,V_3f63007]: ![F, G]: (![X]: s(V_3f63007,happ(s(fun(V_3f63011,V_3f63007),F),s(V_3f63011,X))) = s(V_3f63007,happ(s(fun(V_3f63011,V_3f63007),G),s(V_3f63011,X))) => s(fun(V_3f63011,V_3f63007),F) = s(fun(V_3f63011,V_3f63007),G))).
fof('h4/thm/numpair/nlistrec_thm_e1', conjecture, ![A]: ![T, N, H, F]: s(A,'h4/const/numpair/nlistrec'(s(A,N),s(fun('h4/type/num/num',fun('h4/type/num/num',fun(A,A))),F),s('h4/type/num/num','h4/const/numpair/ncons'(s('h4/type/num/num',H),s('h4/type/num/num',T))))) = s(A,happ(s(fun(A,A),happ(s(fun('h4/type/num/num',fun(A,A)),happ(s(fun('h4/type/num/num',fun('h4/type/num/num',fun(A,A))),F),s('h4/type/num/num',H))),s('h4/type/num/num',T))),s(A,'h4/const/numpair/nlistrec'(s(A,N),s(fun('h4/type/num/num',fun('h4/type/num/num',fun(A,A))),F),s('h4/type/num/num',T)))))).
