%   ORIGINAL: 'h4/thm/seq/SEQ_ABS_IMP_'
% 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: !f l. 'h4/const/seq/-->' f l ==> 'h4/const/seq/-->' (\n. 'h4/const/real/abs' (f n)) ('h4/const/real/abs' l)
%   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: !_0. (!f n. happ (happ _0 f) n = 'h4/const/real/abs' (happ f n)) ==> (!f l. 'h4/const/seq/-->' f l ==> 'h4/const/seq/-->' (happ _0 f) ('h4/const/real/abs' l))
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_3f65036,V_3f65032]: ![F, G]: (![X]: s(V_3f65032,happ(s(fun(V_3f65036,V_3f65032),F),s(V_3f65036,X))) = s(V_3f65032,happ(s(fun(V_3f65036,V_3f65032),G),s(V_3f65036,X))) => s(fun(V_3f65036,V_3f65032),F) = s(fun(V_3f65036,V_3f65032),G))).
fof('h4/thm/seq/SEQ_ABS_IMP_', conjecture, ![V__0]: (![F, N]: s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),happ(s(fun(fun('h4/type/num/num','h4/type/realax/real'),fun('h4/type/num/num','h4/type/realax/real')),V__0),s(fun('h4/type/num/num','h4/type/realax/real'),F))),s('h4/type/num/num',N))) = s('h4/type/realax/real','h4/const/real/abs'(s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),F),s('h4/type/num/num',N))))) => ![F, L]: (p(s(bool,'h4/const/seq/-->'(s(fun('h4/type/num/num','h4/type/realax/real'),F),s('h4/type/realax/real',L)))) => p(s(bool,'h4/const/seq/-->'(s(fun('h4/type/num/num','h4/type/realax/real'),happ(s(fun(fun('h4/type/num/num','h4/type/realax/real'),fun('h4/type/num/num','h4/type/realax/real')),V__0),s(fun('h4/type/num/num','h4/type/realax/real'),F))),s('h4/type/realax/real','h4/const/real/abs'(s('h4/type/realax/real',L))))))))).
