%   ORIGINAL: 'h4/thm/transc/SQRT_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: !x y. 'h4/const/real/real_lte' ('h4/const/real/real_of_num' 'h4/const/num/0') x /\ 'h4/const/real/real_lte' ('h4/const/real/real_of_num' 'h4/const/num/0') y ==> 'h4/const/transc/sqrt' ('h4/const/real/#slash#' x y) = 'h4/const/real/#slash#' ('h4/const/transc/sqrt' x) ('h4/const/transc/sqrt' 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: !x y. 'h4/const/real/real_lte' ('h4/const/real/real_of_num' 'h4/const/num/0') x /\ 'h4/const/real/real_lte' ('h4/const/real/real_of_num' 'h4/const/num/0') y ==> 'h4/const/transc/sqrt' ('h4/const/real/#slash#' x y) = 'h4/const/real/#slash#' ('h4/const/transc/sqrt' x) ('h4/const/transc/sqrt' 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_3f69936,V_3f69932]: ![F, G]: (![X]: s(V_3f69932,happ(s(fun(V_3f69936,V_3f69932),F),s(V_3f69936,X))) = s(V_3f69932,happ(s(fun(V_3f69936,V_3f69932),G),s(V_3f69936,X))) => s(fun(V_3f69936,V_3f69932),F) = s(fun(V_3f69936,V_3f69932),G))).
fof('h4/thm/transc/SQRT_DIV_', conjecture, ![X, Y]: ((p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0'))),s('h4/type/realax/real',X)))) & p(s(bool,'h4/const/real/real_lte'(s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0'))),s('h4/type/realax/real',Y))))) => s('h4/type/realax/real','h4/const/transc/sqrt'(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/transc/sqrt'(s('h4/type/realax/real',X))),s('h4/type/realax/real','h4/const/transc/sqrt'(s('h4/type/realax/real',Y))))))).
