%   ORIGINAL: 'h4/thm/numeral/iSUB_THM_2'
% 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/iSUB' F ('h4/const/arithmetic/BIT1' n) 'h4/const/arithmetic/ZERO' = 'h4/const/numeral/iDUB' 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/iSUB' F ('h4/const/arithmetic/BIT1' n) 'h4/const/arithmetic/ZERO' = 'h4/const/numeral/iDUB' 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_3f44284,V_3f44280]: ![F, G]: (![X]: s(V_3f44280,happ(s(fun(V_3f44284,V_3f44280),F),s(V_3f44284,X))) = s(V_3f44280,happ(s(fun(V_3f44284,V_3f44280),G),s(V_3f44284,X))) => s(fun(V_3f44284,V_3f44280),F) = s(fun(V_3f44284,V_3f44280),G))).
fof('h4/thm/numeral/iSUB_THM_2', conjecture, ![N]: s('h4/type/num/num','h4/const/numeral/iSUB'(s(bool,'F'),s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num',N))),s('h4/type/num/num','h4/const/arithmetic/ZERO'))) = s('h4/type/num/num','h4/const/numeral/iDUB'(s('h4/type/num/num',N)))).
