%   ORIGINAL: 'h4/thm/seq/SER_LE_'
% 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 g. (!n. 'h4/const/real/real_lte' (f n) (g n)) /\ 'h4/const/seq/summable' f /\ 'h4/const/seq/summable' g ==> 'h4/const/real/real_lte' ('h4/const/seq/suminf' f) ('h4/const/seq/suminf' g)
%   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: !f g. (!n. 'h4/const/real/real_lte' (happ f n) (happ g n)) /\ 'h4/const/seq/summable' f /\ 'h4/const/seq/summable' g ==> 'h4/const/real/real_lte' ('h4/const/seq/suminf' f) ('h4/const/seq/suminf' g)
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_3f65686,V_3f65682]: ![F, G]: (![X]: s(V_3f65682,happ(s(fun(V_3f65686,V_3f65682),F),s(V_3f65686,X))) = s(V_3f65682,happ(s(fun(V_3f65686,V_3f65682),G),s(V_3f65686,X))) => s(fun(V_3f65686,V_3f65682),F) = s(fun(V_3f65686,V_3f65682),G))).
fof('h4/thm/seq/SER_LE_', conjecture, ![F, G]: ((![N]: p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),F),s('h4/type/num/num',N))),s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),G),s('h4/type/num/num',N)))))) & (p(s(bool,'h4/const/seq/summable'(s(fun('h4/type/num/num','h4/type/realax/real'),F)))) & p(s(bool,'h4/const/seq/summable'(s(fun('h4/type/num/num','h4/type/realax/real'),G)))))) => p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real','h4/const/seq/suminf'(s(fun('h4/type/num/num','h4/type/realax/real'),F))),s('h4/type/realax/real','h4/const/seq/suminf'(s(fun('h4/type/num/num','h4/type/realax/real'),G)))))))).
