%   ORIGINAL: 'h4/thm/nets/MTOP_TENDS_'
% 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: !d g x x0. 'h4/const/nets/tends' x x0 ('h4/const/pair/,' ('h4/const/topology/mtop' d) g) <=> (!e. 'h4/const/realax/real_lt' ('h4/const/real/real_of_num' 'h4/const/num/0') e ==> (?n. g n n /\ (!m. g m n ==> 'h4/const/realax/real_lt' ('h4/const/topology/dist' d ('h4/const/pair/,' (x m) x0)) e)))
%   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: !d g x x0. 'h4/const/nets/tends' x x0 ('h4/const/pair/,' ('h4/const/topology/mtop' d) g) <=> (!e. 'h4/const/realax/real_lt' ('h4/const/real/real_of_num' 'h4/const/num/0') e ==> (?n. happ (happ g n) n /\ (!m. happ (happ g m) n ==> 'h4/const/realax/real_lt' ('h4/const/topology/dist' d ('h4/const/pair/,' (happ x m) x0)) e)))
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_3f63811,V_3f63807]: ![F, G]: (![X]: s(V_3f63807,happ(s(fun(V_3f63811,V_3f63807),F),s(V_3f63811,X))) = s(V_3f63807,happ(s(fun(V_3f63811,V_3f63807),G),s(V_3f63811,X))) => s(fun(V_3f63811,V_3f63807),F) = s(fun(V_3f63811,V_3f63807),G))).
fof('h4/thm/nets/MTOP_TENDS_', conjecture, ![B,A]: ![D, G, X, X0]: (p(s(bool,'h4/const/nets/tends'(s(fun(B,A),X),s(A,X0),s('h4/type/pair/prod'('h4/type/topology/topology'(A),fun(B,fun(B,bool))),'h4/const/pair/,'(s('h4/type/topology/topology'(A),'h4/const/topology/mtop'(s('h4/type/topology/metric'(A),D))),s(fun(B,fun(B,bool)),G)))))) <=> ![E]: (p(s(bool,'h4/const/realax/real_lt'(s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0'))),s('h4/type/realax/real',E)))) => ?[N]: (p(s(bool,happ(s(fun(B,bool),happ(s(fun(B,fun(B,bool)),G),s(B,N))),s(B,N)))) & ![M]: (p(s(bool,happ(s(fun(B,bool),happ(s(fun(B,fun(B,bool)),G),s(B,M))),s(B,N)))) => p(s(bool,'h4/const/realax/real_lt'(s('h4/type/realax/real','h4/const/topology/dist'(s('h4/type/topology/metric'(A),D),s('h4/type/pair/prod'(A,A),'h4/const/pair/,'(s(A,happ(s(fun(B,A),X),s(B,M))),s(A,X0))))),s('h4/type/realax/real',E))))))))).
