%   ORIGINAL: 'h4/thm/numeral/onecount_characterisation_'
% 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 a. 'h4/const/prim_rec/<' 'h4/const/num/0' ('h4/const/numeral/onecount' n a) /\ 'h4/const/prim_rec/<' 'h4/const/num/0' n ==> n = 'h4/const/arithmetic/-' ('h4/const/arithmetic/EXP' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT2' 'h4/const/arithmetic/ZERO')) ('h4/const/arithmetic/-' ('h4/const/numeral/onecount' n a) a)) ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))
%   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 a. 'h4/const/prim_rec/<' 'h4/const/num/0' ('h4/const/numeral/onecount' n a) /\ 'h4/const/prim_rec/<' 'h4/const/num/0' n ==> n = 'h4/const/arithmetic/-' ('h4/const/arithmetic/EXP' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT2' 'h4/const/arithmetic/ZERO')) ('h4/const/arithmetic/-' ('h4/const/numeral/onecount' n a) a)) ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))
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_3f45659,V_3f45655]: ![F, G]: (![X]: s(V_3f45655,happ(s(fun(V_3f45659,V_3f45655),F),s(V_3f45659,X))) = s(V_3f45655,happ(s(fun(V_3f45659,V_3f45655),G),s(V_3f45659,X))) => s(fun(V_3f45659,V_3f45655),F) = s(fun(V_3f45659,V_3f45655),G))).
fof('h4/thm/numeral/onecount_characterisation_', conjecture, ![N, A]: ((p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num','h4/const/num/0'),s('h4/type/num/num','h4/const/numeral/onecount'(s('h4/type/num/num',N),s('h4/type/num/num',A)))))) & p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num','h4/const/num/0'),s('h4/type/num/num',N))))) => s('h4/type/num/num',N) = s('h4/type/num/num','h4/const/arithmetic/-'(s('h4/type/num/num','h4/const/arithmetic/EXP'(s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT2'(s('h4/type/num/num','h4/const/arithmetic/ZERO'))))),s('h4/type/num/num','h4/const/arithmetic/-'(s('h4/type/num/num','h4/const/numeral/onecount'(s('h4/type/num/num',N),s('h4/type/num/num',A))),s('h4/type/num/num',A))))),s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num','h4/const/arithmetic/ZERO'))))))))).
