%   ORIGINAL: 'h4/thm/real/ABS_DIV_'
% 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: !y. ~(y = 'h4/const/real/real_of_num' 'h4/const/num/0') ==> (!x. 'h4/const/real/abs' ('h4/const/real/#slash#' x y) = 'h4/const/real/#slash#' ('h4/const/real/abs' x) ('h4/const/real/abs' y))
%   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: !y. ~(y = 'h4/const/real/real_of_num' 'h4/const/num/0') ==> (!x. 'h4/const/real/abs' ('h4/const/real/#slash#' x y) = 'h4/const/real/#slash#' ('h4/const/real/abs' x) ('h4/const/real/abs' y))
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_3f92744,V_3f92740]: ![F, G]: (![X]: s(V_3f92740,happ(s(fun(V_3f92744,V_3f92740),F),s(V_3f92744,X))) = s(V_3f92740,happ(s(fun(V_3f92744,V_3f92740),G),s(V_3f92744,X))) => s(fun(V_3f92744,V_3f92740),F) = s(fun(V_3f92744,V_3f92740),G))).
fof('h4/thm/real/ABS_DIV_', conjecture, ![Y]: (~ (s('h4/type/realax/real',Y) = s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0')))) => ![X]: s('h4/type/realax/real','h4/const/real/abs'(s('h4/type/realax/real','h4/const/real/#slash#'(s('h4/type/realax/real',X),s('h4/type/realax/real',Y))))) = s('h4/type/realax/real','h4/const/real/#slash#'(s('h4/type/realax/real','h4/const/real/abs'(s('h4/type/realax/real',X))),s('h4/type/realax/real','h4/const/real/abs'(s('h4/type/realax/real',Y))))))).
