%   ORIGINAL: 'h4/thm/real/eq_rat_'
% 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 x v u. 'h4/const/real/#slash#' x y = 'h4/const/real/#slash#' u v <=> 'h4/const/bool/COND' (y = 'h4/const/real/real_of_num' 'h4/const/num/0') ('h4/const/marker/unint' ('h4/const/real/#slash#' x y) = 'h4/const/real/#slash#' u v) ('h4/const/bool/COND' (v = 'h4/const/real/real_of_num' 'h4/const/num/0') ('h4/const/real/#slash#' x y = 'h4/const/marker/unint' ('h4/const/real/#slash#' u v)) ('h4/const/bool/COND' (y = v) (x = u) ('h4/const/realax/real_mul' x v = 'h4/const/realax/real_mul' y u)))
%   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 x v u. 'h4/const/real/#slash#' x y = 'h4/const/real/#slash#' u v <=> (?v. (v <=> 'h4/const/marker/unint' ('h4/const/real/#slash#' x y) = 'h4/const/real/#slash#' u v) /\ (?v'. (v' <=> y = 'h4/const/real/real_of_num' 'h4/const/num/0') /\ (?v''. (v'' <=> 'h4/const/realax/real_mul' x v = 'h4/const/realax/real_mul' y u) /\ (?v'''. (v''' <=> x = u) /\ (?v''''. (v'''' <=> y = v) /\ (?v'''''. (v''''' <=> 'h4/const/real/#slash#' x y = 'h4/const/marker/unint' ('h4/const/real/#slash#' u v)) /\ (?v''''''. (v'''''' <=> v = 'h4/const/real/real_of_num' 'h4/const/num/0') /\ 'h4/const/bool/COND' v' v ('h4/const/bool/COND' v'''''' v''''' ('h4/const/bool/COND' v'''' v''' v'')))))))))
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_3f98106,V_3f98102]: ![F, G]: (![X]: s(V_3f98102,happ(s(fun(V_3f98106,V_3f98102),F),s(V_3f98106,X))) = s(V_3f98102,happ(s(fun(V_3f98106,V_3f98102),G),s(V_3f98106,X))) => s(fun(V_3f98106,V_3f98102),F) = s(fun(V_3f98106,V_3f98102),G))).
fof('h4/thm/real/eq_rat_', conjecture, ![Y, X, V, U]: (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',U),s('h4/type/realax/real',V))) <=> ?[V0]: ((p(s(bool,V0)) <=> s('h4/type/realax/real','h4/const/marker/unint'(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',U),s('h4/type/realax/real',V)))) & ?[V_27]: ((p(s(bool,V_27)) <=> 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')))) & ?[V_27_27]: ((p(s(bool,V_27_27)) <=> s('h4/type/realax/real','h4/const/realax/real_mul'(s('h4/type/realax/real',X),s('h4/type/realax/real',V))) = s('h4/type/realax/real','h4/const/realax/real_mul'(s('h4/type/realax/real',Y),s('h4/type/realax/real',U)))) & ?[V_27_27_27]: ((p(s(bool,V_27_27_27)) <=> s('h4/type/realax/real',X) = s('h4/type/realax/real',U)) & ?[V_27_27_27_27]: ((p(s(bool,V_27_27_27_27)) <=> s('h4/type/realax/real',Y) = s('h4/type/realax/real',V)) & ?[V_27_27_27_27_27]: ((p(s(bool,V_27_27_27_27_27)) <=> 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/marker/unint'(s('h4/type/realax/real','h4/const/real/#slash#'(s('h4/type/realax/real',U),s('h4/type/realax/real',V)))))) & ?[V_27_27_27_27_27_27]: ((p(s(bool,V_27_27_27_27_27_27)) <=> s('h4/type/realax/real',V) = s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0')))) & p(s(bool,'h4/const/bool/COND'(s(bool,V_27),s(bool,V0),s(bool,'h4/const/bool/COND'(s(bool,V_27_27_27_27_27_27),s(bool,V_27_27_27_27_27),s(bool,'h4/const/bool/COND'(s(bool,V_27_27_27_27),s(bool,V_27_27_27),s(bool,V_27_27))))))))))))))))).
