%   ORIGINAL: 'h4/thm/realax/TREAL_ADD_LINV_'
% 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: !x. 'h4/const/realax/treal_eq' ('h4/const/realax/treal_add' ('h4/const/realax/treal_neg' x) x) 'h4/const/realax/treal_0'
%   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: !x. 'h4/const/realax/treal_eq' ('h4/const/realax/treal_add' ('h4/const/realax/treal_neg' x) x) 'h4/const/realax/treal_0'
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_3f49361,V_3f49357]: ![F, G]: (![X]: s(V_3f49357,happ(s(fun(V_3f49361,V_3f49357),F),s(V_3f49361,X))) = s(V_3f49357,happ(s(fun(V_3f49361,V_3f49357),G),s(V_3f49361,X))) => s(fun(V_3f49361,V_3f49357),F) = s(fun(V_3f49361,V_3f49357),G))).
fof('h4/thm/realax/TREAL_ADD_LINV_', conjecture, ![X]: p(s(bool,'h4/const/realax/treal_eq'(s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),'h4/const/realax/treal_add'(s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),'h4/const/realax/treal_neg'(s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),X))),s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),X))),s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),'h4/const/realax/treal_0'))))).
