%   ORIGINAL: 'h4/thm/pred_set/INSERT_DIFF_'
% 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: !s t x. 'h4/const/pred_set/DIFF' ('h4/const/pred_set/INSERT' x s) t = 'h4/const/bool/COND' ('h4/const/bool/IN' x t) ('h4/const/pred_set/DIFF' s t) ('h4/const/pred_set/INSERT' x ('h4/const/pred_set/DIFF' s t))
%   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: !s t x. 'h4/const/pred_set/DIFF' ('h4/const/pred_set/INSERT' x s) t = 'h4/const/bool/COND' ('h4/const/bool/IN' x t) ('h4/const/pred_set/DIFF' s t) ('h4/const/pred_set/INSERT' x ('h4/const/pred_set/DIFF' s t))
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_3f17069,V_3f17065]: ![F, G]: (![X]: s(V_3f17065,happ(s(fun(V_3f17069,V_3f17065),F),s(V_3f17069,X))) = s(V_3f17065,happ(s(fun(V_3f17069,V_3f17065),G),s(V_3f17069,X))) => s(fun(V_3f17069,V_3f17065),F) = s(fun(V_3f17069,V_3f17065),G))).
fof('h4/thm/pred_set/INSERT_DIFF_', conjecture, ![A]: ![S, T, X]: s(fun(A,bool),'h4/const/pred_set/DIFF'(s(fun(A,bool),'h4/const/pred_set/INSERT'(s(A,X),s(fun(A,bool),S))),s(fun(A,bool),T))) = s(fun(A,bool),'h4/const/bool/COND'(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),T))),s(fun(A,bool),'h4/const/pred_set/DIFF'(s(fun(A,bool),S),s(fun(A,bool),T))),s(fun(A,bool),'h4/const/pred_set/INSERT'(s(A,X),s(fun(A,bool),'h4/const/pred_set/DIFF'(s(fun(A,bool),S),s(fun(A,bool),T)))))))).
