%   ORIGINAL: 'h4/thm/pred_set/MIN_SET_THM_e1'
% 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 e1 e2. 'h4/const/pred_set/MIN_SET' ('h4/const/pred_set/INSERT' e1 ('h4/const/pred_set/INSERT' e2 s)) = 'h4/const/arithmetic/MIN' e1 ('h4/const/pred_set/MIN_SET' ('h4/const/pred_set/INSERT' e2 s))
%   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 e1 e2. 'h4/const/pred_set/MIN_SET' ('h4/const/pred_set/INSERT' e1 ('h4/const/pred_set/INSERT' e2 s)) = 'h4/const/arithmetic/MIN' e1 ('h4/const/pred_set/MIN_SET' ('h4/const/pred_set/INSERT' e2 s))
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_3f23023,V_3f23019]: ![F, G]: (![X]: s(V_3f23019,happ(s(fun(V_3f23023,V_3f23019),F),s(V_3f23023,X))) = s(V_3f23019,happ(s(fun(V_3f23023,V_3f23019),G),s(V_3f23023,X))) => s(fun(V_3f23023,V_3f23019),F) = s(fun(V_3f23023,V_3f23019),G))).
fof('h4/thm/pred_set/MIN_SET_THM_e1', conjecture, ![S, E1, E2]: s('h4/type/num/num','h4/const/pred_set/MIN_SET'(s(fun('h4/type/num/num',bool),'h4/const/pred_set/INSERT'(s('h4/type/num/num',E1),s(fun('h4/type/num/num',bool),'h4/const/pred_set/INSERT'(s('h4/type/num/num',E2),s(fun('h4/type/num/num',bool),S))))))) = s('h4/type/num/num','h4/const/arithmetic/MIN'(s('h4/type/num/num',E1),s('h4/type/num/num','h4/const/pred_set/MIN_SET'(s(fun('h4/type/num/num',bool),'h4/const/pred_set/INSERT'(s('h4/type/num/num',E2),s(fun('h4/type/num/num',bool),S)))))))).
