%   ORIGINAL: h4/topology/METRIC__ISMET
% 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
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/topology/metric__tybij_c0: !a. h4/topology/metric0 (h4/topology/dist a) = a
% Assm: h4/topology/metric__tybij_c1: !r. h4/topology/ismet r <=> h4/topology/dist (h4/topology/metric0 r) = r
% Goal: !m. h4/topology/ismet (h4/topology/dist m)
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_topologys_metricu_u_tybiju_c0]: !a. h4/topology/metric0 (h4/topology/dist a) = a
% Assm [h4s_topologys_metricu_u_tybiju_c1]: !r. h4/topology/ismet r <=> h4/topology/dist (h4/topology/metric0 r) = r
% Goal: !m. h4/topology/ismet (h4/topology/dist m)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q352227,TV_Q352223]: ![V_f, V_g]: (![V_x]: s(TV_Q352223,happ(s(t_fun(TV_Q352227,TV_Q352223),V_f),s(TV_Q352227,V_x))) = s(TV_Q352223,happ(s(t_fun(TV_Q352227,TV_Q352223),V_g),s(TV_Q352227,V_x))) => s(t_fun(TV_Q352227,TV_Q352223),V_f) = s(t_fun(TV_Q352227,TV_Q352223),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_topologys_metricu_u_tybiju_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_topologys_metric(TV_u_27a),h4s_topologys_metric0(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),t_h4s_realaxs_real),h4s_topologys_dist(s(t_h4s_topologys_metric(TV_u_27a),V_a))))) = s(t_h4s_topologys_metric(TV_u_27a),V_a)).
fof(ah4s_topologys_metricu_u_tybiju_c1, axiom, ![TV_u_27a]: ![V_r]: (p(s(t_bool,h4s_topologys_ismet(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),t_h4s_realaxs_real),V_r)))) <=> s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),t_h4s_realaxs_real),h4s_topologys_dist(s(t_h4s_topologys_metric(TV_u_27a),h4s_topologys_metric0(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),t_h4s_realaxs_real),V_r))))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),t_h4s_realaxs_real),V_r))).
fof(ch4s_topologys_METRICu_u_ISMET, conjecture, ![TV_u_27a]: ![V_m]: p(s(t_bool,h4s_topologys_ismet(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),t_h4s_realaxs_real),h4s_topologys_dist(s(t_h4s_topologys_metric(TV_u_27a),V_m))))))).
