%   ORIGINAL: 'h4/thm/numpair/invtri0_def_'
% 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/numpair/invtri0' n a = 'h4/const/bool/COND' ('h4/const/prim_rec/<' n ('h4/const/arithmetic/+' a ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')))) ('h4/const/pair/,' n a) ('h4/const/numpair/invtri0' ('h4/const/arithmetic/-' n ('h4/const/arithmetic/+' a ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')))) ('h4/const/arithmetic/+' 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/numpair/invtri0' n a = 'h4/const/bool/COND' ('h4/const/prim_rec/<' n ('h4/const/arithmetic/+' a ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')))) ('h4/const/pair/,' n a) ('h4/const/numpair/invtri0' ('h4/const/arithmetic/-' n ('h4/const/arithmetic/+' a ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')))) ('h4/const/arithmetic/+' 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_3f62511,V_3f62507]: ![F, G]: (![X]: s(V_3f62507,happ(s(fun(V_3f62511,V_3f62507),F),s(V_3f62511,X))) = s(V_3f62507,happ(s(fun(V_3f62511,V_3f62507),G),s(V_3f62511,X))) => s(fun(V_3f62511,V_3f62507),F) = s(fun(V_3f62511,V_3f62507),G))).
fof('h4/thm/numpair/invtri0_def_', conjecture, ![N, A]: s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),'h4/const/numpair/invtri0'(s('h4/type/num/num',N),s('h4/type/num/num',A))) = s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),'h4/const/bool/COND'(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num',N),s('h4/type/num/num','h4/const/arithmetic/+'(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'))))))))),s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),'h4/const/pair/,'(s('h4/type/num/num',N),s('h4/type/num/num',A))),s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),'h4/const/numpair/invtri0'(s('h4/type/num/num','h4/const/arithmetic/-'(s('h4/type/num/num',N),s('h4/type/num/num','h4/const/arithmetic/+'(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'))))))))),s('h4/type/num/num','h4/const/arithmetic/+'(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')))))))))))).
