%   ORIGINAL: 'h4/thm/seq/SEQ_ICONV_'
% 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/>=') f /\ (!m n. 'h4/const/arithmetic/>=' m n ==> 'h4/const/real/real_ge' (f m) (f n)) ==> 'h4/const/seq/convergent' 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: !f. 'h4/const/nets/bounded' ('h4/const/pair/,' 'h4/const/topology/mr1' 'h4/const/arithmetic/>=') f /\ (!m n. happ (happ 'h4/const/arithmetic/>=' m) n ==> 'h4/const/real/real_ge' (happ f m) (happ f n)) ==> 'h4/const/seq/convergent' 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_3f64736,V_3f64732]: ![F, G]: (![X]: s(V_3f64732,happ(s(fun(V_3f64736,V_3f64732),F),s(V_3f64736,X))) = s(V_3f64732,happ(s(fun(V_3f64736,V_3f64732),G),s(V_3f64736,X))) => s(fun(V_3f64736,V_3f64732),F) = s(fun(V_3f64736,V_3f64732),G))).
fof('h4/thm/seq/SEQ_ICONV_', conjecture, ![F]: ((p(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)))) & ![M, N]: (p(s(bool,happ(s(fun('h4/type/num/num',bool),happ(s(fun('h4/type/num/num',fun('h4/type/num/num',bool)),'h4/const/arithmetic/>='),s('h4/type/num/num',M))),s('h4/type/num/num',N)))) => p(s(bool,'h4/const/real/real_ge'(s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),F),s('h4/type/num/num',M))),s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),F),s('h4/type/num/num',N)))))))) => p(s(bool,'h4/const/seq/convergent'(s(fun('h4/type/num/num','h4/type/realax/real'),F)))))).
