%   ORIGINAL: 'h4/thm/topology/TOPOLOGY_UNION_'
% 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: !L P. 'h4/const/pred_set/SUBSET' P ('h4/const/topology/open' L) ==> 'h4/const/topology/open' L ('h4/const/pred_set/BIGUNION' P)
%   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: !L P. 'h4/const/pred_set/SUBSET' P ('h4/const/topology/open' L) ==> happ ('h4/const/topology/open' L) ('h4/const/pred_set/BIGUNION' P)
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_3f37529,V_3f37525]: ![F, G]: (![X]: s(V_3f37525,happ(s(fun(V_3f37529,V_3f37525),F),s(V_3f37529,X))) = s(V_3f37525,happ(s(fun(V_3f37529,V_3f37525),G),s(V_3f37529,X))) => s(fun(V_3f37529,V_3f37525),F) = s(fun(V_3f37529,V_3f37525),G))).
fof('h4/thm/topology/TOPOLOGY_UNION_', conjecture, ![A]: ![L, P]: (p(s(bool,'h4/const/pred_set/SUBSET'(s(fun(fun(A,bool),bool),P),s(fun(fun(A,bool),bool),'h4/const/topology/open'(s('h4/type/topology/topology'(A),L)))))) => p(s(bool,happ(s(fun(fun(A,bool),bool),'h4/const/topology/open'(s('h4/type/topology/topology'(A),L))),s(fun(A,bool),'h4/const/pred_set/BIGUNION'(s(fun(fun(A,bool),bool),P)))))))).
