%   ORIGINAL: 'h4/thm/real/le_ratr_'
% 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 u m. 'h4/const/real/real_lte' x ('h4/const/real/#slash#' u ('h4/const/real/real_of_num' m)) <=> 'h4/const/bool/COND' (m = 'h4/const/num/0') ('h4/const/real/real_lte' x ('h4/const/marker/unint' ('h4/const/real/#slash#' u ('h4/const/real/real_of_num' 'h4/const/num/0')))) ('h4/const/real/real_lte' ('h4/const/realax/real_mul' ('h4/const/real/real_of_num' m) x) 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: !x u m. ?v. (v <=> m = 'h4/const/num/0') /\ ('h4/const/real/real_lte' x ('h4/const/real/#slash#' u ('h4/const/real/real_of_num' m)) <=> 'h4/const/bool/COND' v ('h4/const/real/real_lte' x ('h4/const/marker/unint' ('h4/const/real/#slash#' u ('h4/const/real/real_of_num' 'h4/const/num/0')))) ('h4/const/real/real_lte' ('h4/const/realax/real_mul' ('h4/const/real/real_of_num' m) x) u))
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_3f98427,V_3f98423]: ![F, G]: (![X]: s(V_3f98423,happ(s(fun(V_3f98427,V_3f98423),F),s(V_3f98427,X))) = s(V_3f98423,happ(s(fun(V_3f98427,V_3f98423),G),s(V_3f98427,X))) => s(fun(V_3f98427,V_3f98423),F) = s(fun(V_3f98427,V_3f98423),G))).
fof('h4/thm/real/le_ratr_', conjecture, ![X, U, M]: ?[V]: ((p(s(bool,V)) <=> s('h4/type/num/num',M) = s('h4/type/num/num','h4/const/num/0')) & s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',X),s('h4/type/realax/real','h4/const/real/#slash#'(s('h4/type/realax/real',U),s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num',M))))))) = s(bool,'h4/const/bool/COND'(s(bool,V),s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real',X),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','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0'))))))))),s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real','h4/const/realax/real_mul'(s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num',M))),s('h4/type/realax/real',X))),s('h4/type/realax/real',U))))))).
