%   ORIGINAL: 'h4/thm/pred_set/BIGINTER_INSERT_'
% 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: !P B. 'h4/const/pred_set/BIGINTER' ('h4/const/pred_set/INSERT' P B) = 'h4/const/pred_set/INTER' P ('h4/const/pred_set/BIGINTER' B)
%   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: !P B. 'h4/const/pred_set/BIGINTER' ('h4/const/pred_set/INSERT' P B) = 'h4/const/pred_set/INTER' P ('h4/const/pred_set/BIGINTER' B)
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_3f20846,V_3f20842]: ![F, G]: (![X]: s(V_3f20842,happ(s(fun(V_3f20846,V_3f20842),F),s(V_3f20846,X))) = s(V_3f20842,happ(s(fun(V_3f20846,V_3f20842),G),s(V_3f20846,X))) => s(fun(V_3f20846,V_3f20842),F) = s(fun(V_3f20846,V_3f20842),G))).
fof('h4/thm/pred_set/BIGINTER_INSERT_', conjecture, ![A]: ![P, B]: s(fun(A,bool),'h4/const/pred_set/BIGINTER'(s(fun(fun(A,bool),bool),'h4/const/pred_set/INSERT'(s(fun(A,bool),P),s(fun(fun(A,bool),bool),B))))) = s(fun(A,bool),'h4/const/pred_set/INTER'(s(fun(A,bool),P),s(fun(A,bool),'h4/const/pred_set/BIGINTER'(s(fun(fun(A,bool),bool),B)))))).
