%   ORIGINAL: 'h4/thm/seq/SEQ_NEG_BOUNDED_'
% 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. 'h4/const/nets/bounded' ('h4/const/pair/,' 'h4/const/topology/mr1' 'h4/const/arithmetic/>=') (\n. 'h4/const/realax/real_neg' (f n)) <=> 'h4/const/nets/bounded' ('h4/const/pair/,' 'h4/const/topology/mr1' 'h4/const/arithmetic/>=') f
%   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/realax/real_neg' (happ f n)) ==> (!f. 'h4/const/nets/bounded' ('h4/const/pair/,' 'h4/const/topology/mr1' 'h4/const/arithmetic/>=') (happ _0 f) <=> 'h4/const/nets/bounded' ('h4/const/pair/,' 'h4/const/topology/mr1' 'h4/const/arithmetic/>=') f)
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_3f64786,V_3f64782]: ![F, G]: (![X]: s(V_3f64782,happ(s(fun(V_3f64786,V_3f64782),F),s(V_3f64786,X))) = s(V_3f64782,happ(s(fun(V_3f64786,V_3f64782),G),s(V_3f64786,X))) => s(fun(V_3f64786,V_3f64782),F) = s(fun(V_3f64786,V_3f64782),G))).
fof('h4/thm/seq/SEQ_NEG_BOUNDED_', 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/realax/real_neg'(s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),F),s('h4/type/num/num',N))))) => ![F]: s(bool,'h4/const/nets/bounded'(s('h4/type/pair/prod'('h4/type/topology/metric'('h4/type/realax/real'),fun('h4/type/num/num',fun('h4/type/num/num',bool))),'h4/const/pair/,'(s('h4/type/topology/metric'('h4/type/realax/real'),'h4/const/topology/mr1'),s(fun('h4/type/num/num',fun('h4/type/num/num',bool)),'h4/const/arithmetic/>='))),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(bool,'h4/const/nets/bounded'(s('h4/type/pair/prod'('h4/type/topology/metric'('h4/type/realax/real'),fun('h4/type/num/num',fun('h4/type/num/num',bool))),'h4/const/pair/,'(s('h4/type/topology/metric'('h4/type/realax/real'),'h4/const/topology/mr1'),s(fun('h4/type/num/num',fun('h4/type/num/num',bool)),'h4/const/arithmetic/>='))),s(fun('h4/type/num/num','h4/type/realax/real'),F))))).
