%   ORIGINAL: 'h4/thm/numeral/numeral_iisuc_e2'
% 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: !n. 'h4/const/numeral/iiSUC' ('h4/const/arithmetic/BIT2' n) = 'h4/const/arithmetic/BIT2' ('h4/const/num/SUC' n)
%   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: !n. 'h4/const/numeral/iiSUC' ('h4/const/arithmetic/BIT2' n) = 'h4/const/arithmetic/BIT2' ('h4/const/num/SUC' n)
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_3f43034,V_3f43030]: ![F, G]: (![X]: s(V_3f43030,happ(s(fun(V_3f43034,V_3f43030),F),s(V_3f43034,X))) = s(V_3f43030,happ(s(fun(V_3f43034,V_3f43030),G),s(V_3f43034,X))) => s(fun(V_3f43034,V_3f43030),F) = s(fun(V_3f43034,V_3f43030),G))).
fof('h4/thm/numeral/numeral_iisuc_e2', conjecture, ![N]: s('h4/type/num/num','h4/const/numeral/iiSUC'(s('h4/type/num/num','h4/const/arithmetic/BIT2'(s('h4/type/num/num',N))))) = s('h4/type/num/num','h4/const/arithmetic/BIT2'(s('h4/type/num/num','h4/const/num/SUC'(s('h4/type/num/num',N)))))).
