%   ORIGINAL: h4/topology/METRIC__SAME
% 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__ZERO: !y x m. h4/topology/dist m (h4/pair/_2C x y) = h4/real/real__of__num h4/num/0 <=> x = y
% Goal: !x m. h4/topology/dist m (h4/pair/_2C x x) = h4/real/real__of__num h4/num/0
%   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_ZERO]: !y x m. h4/topology/dist m (h4/pair/_2C x y) = h4/real/real__of__num h4/num/0 <=> x = y
% Goal: !x m. h4/topology/dist m (h4/pair/_2C x x) = h4/real/real__of__num h4/num/0
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_Q352277,TV_Q352273]: ![V_f, V_g]: (![V_x]: s(TV_Q352273,happ(s(t_fun(TV_Q352277,TV_Q352273),V_f),s(TV_Q352277,V_x))) = s(TV_Q352273,happ(s(t_fun(TV_Q352277,TV_Q352273),V_g),s(TV_Q352277,V_x))) => s(t_fun(TV_Q352277,TV_Q352273),V_f) = s(t_fun(TV_Q352277,TV_Q352273),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_ZERO, axiom, ![TV_u_27a]: ![V_y, V_x, V_m]: (s(t_h4s_realaxs_real,h4s_topologys_dist(s(t_h4s_topologys_metric(TV_u_27a),V_m),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27a,V_y))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ch4s_topologys_METRICu_u_SAME, conjecture, ![TV_u_27a]: ![V_x, V_m]: s(t_h4s_realaxs_real,h4s_topologys_dist(s(t_h4s_topologys_metric(TV_u_27a),V_m),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27a,V_x))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
