%   ORIGINAL: 'h4/thm/numpair/nmap_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 h f. 'h4/const/numpair/nmap' f ('h4/const/numpair/ncons' h t) = 'h4/const/numpair/ncons' (f h) ('h4/const/numpair/nmap' 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 h f. 'h4/const/numpair/nmap' f ('h4/const/numpair/ncons' h t) = 'h4/const/numpair/ncons' (happ f h) ('h4/const/numpair/nmap' 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_3f63136,V_3f63132]: ![F, G]: (![X]: s(V_3f63132,happ(s(fun(V_3f63136,V_3f63132),F),s(V_3f63136,X))) = s(V_3f63132,happ(s(fun(V_3f63136,V_3f63132),G),s(V_3f63136,X))) => s(fun(V_3f63136,V_3f63132),F) = s(fun(V_3f63136,V_3f63132),G))).
fof('h4/thm/numpair/nmap_thm_e1', conjecture, ![T, H, F]: s('h4/type/num/num','h4/const/numpair/nmap'(s(fun('h4/type/num/num','h4/type/num/num'),F),s('h4/type/num/num','h4/const/numpair/ncons'(s('h4/type/num/num',H),s('h4/type/num/num',T))))) = s('h4/type/num/num','h4/const/numpair/ncons'(s('h4/type/num/num',happ(s(fun('h4/type/num/num','h4/type/num/num'),F),s('h4/type/num/num',H))),s('h4/type/num/num','h4/const/numpair/nmap'(s(fun('h4/type/num/num','h4/type/num/num'),F),s('h4/type/num/num',T)))))).
