%   ORIGINAL: 'h4/thm/nets/NET_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: !g. 'h4/const/nets/dorder' g ==> (!x x0 y y0. 'h4/const/nets/tends' x x0 ('h4/const/pair/,' ('h4/const/topology/mtop' 'h4/const/topology/mr1') g) /\ 'h4/const/nets/tends' y y0 ('h4/const/pair/,' ('h4/const/topology/mtop' 'h4/const/topology/mr1') g) /\ (?N. g N N /\ (!n. g n N ==> 'h4/const/real/real_lte' (x n) (y n))) ==> 'h4/const/real/real_lte' x0 y0)
%   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: !g. 'h4/const/nets/dorder' g ==> (!x x0 y y0. 'h4/const/nets/tends' x x0 ('h4/const/pair/,' ('h4/const/topology/mtop' 'h4/const/topology/mr1') g) /\ 'h4/const/nets/tends' y y0 ('h4/const/pair/,' ('h4/const/topology/mtop' 'h4/const/topology/mr1') g) /\ (?N. happ (happ g N) N /\ (!n. happ (happ g n) N ==> 'h4/const/real/real_lte' (happ x n) (happ y n))) ==> 'h4/const/real/real_lte' x0 y0)
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_3f64311,V_3f64307]: ![F, G]: (![X]: s(V_3f64307,happ(s(fun(V_3f64311,V_3f64307),F),s(V_3f64311,X))) = s(V_3f64307,happ(s(fun(V_3f64311,V_3f64307),G),s(V_3f64311,X))) => s(fun(V_3f64311,V_3f64307),F) = s(fun(V_3f64311,V_3f64307),G))).
fof('h4/thm/nets/NET_LE_', conjecture, ![A]: ![G]: (p(s(bool,'h4/const/nets/dorder'(s(fun(A,fun(A,bool)),G)))) => ![X, X0, Y, Y0]: ((p(s(bool,'h4/const/nets/tends'(s(fun(A,'h4/type/realax/real'),X),s('h4/type/realax/real',X0),s('h4/type/pair/prod'('h4/type/topology/topology'('h4/type/realax/real'),fun(A,fun(A,bool))),'h4/const/pair/,'(s('h4/type/topology/topology'('h4/type/realax/real'),'h4/const/topology/mtop'(s('h4/type/topology/metric'('h4/type/realax/real'),'h4/const/topology/mr1'))),s(fun(A,fun(A,bool)),G)))))) & (p(s(bool,'h4/const/nets/tends'(s(fun(A,'h4/type/realax/real'),Y),s('h4/type/realax/real',Y0),s('h4/type/pair/prod'('h4/type/topology/topology'('h4/type/realax/real'),fun(A,fun(A,bool))),'h4/const/pair/,'(s('h4/type/topology/topology'('h4/type/realax/real'),'h4/const/topology/mtop'(s('h4/type/topology/metric'('h4/type/realax/real'),'h4/const/topology/mr1'))),s(fun(A,fun(A,bool)),G)))))) & ?[N]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),G),s(A,N))),s(A,N)))) & ![N0]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),G),s(A,N0))),s(A,N)))) => p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',happ(s(fun(A,'h4/type/realax/real'),X),s(A,N0))),s('h4/type/realax/real',happ(s(fun(A,'h4/type/realax/real'),Y),s(A,N0)))))))))) => p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',X0),s('h4/type/realax/real',Y0))))))).
