%   ORIGINAL: h4/listRange/LENGTH__listRangeLHI
% 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/list/LENGTH__GENLIST: !n f. h4/list/LENGTH (h4/list/GENLIST f n) = n
% Assm: h4/listRange/listRangeLHI__def: !n m. h4/listRange/listRangeLHI m n = h4/list/GENLIST (\i. h4/arithmetic/_2B m i) (h4/arithmetic/_2D n m)
% Goal: !lo hi. h4/list/LENGTH (h4/listRange/listRangeLHI lo hi) = h4/arithmetic/_2D hi lo
%   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_lists_LENGTHu_u_GENLIST]: !n f. h4/list/LENGTH (h4/list/GENLIST f n) = n
% Assm [h4s_listRanges_listRangeLHIu_u_def]: !_0. (!m i. happ (happ _0 m) i = h4/arithmetic/_2B m i) ==> (!n m. h4/listRange/listRangeLHI m n = h4/list/GENLIST (happ _0 m) (h4/arithmetic/_2D n m))
% Goal: !lo hi. h4/list/LENGTH (h4/listRange/listRangeLHI lo hi) = h4/arithmetic/_2D hi lo
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_Q72295,TV_Q72291]: ![V_f, V_g]: (![V_x]: s(TV_Q72291,happ(s(t_fun(TV_Q72295,TV_Q72291),V_f),s(TV_Q72295,V_x))) = s(TV_Q72291,happ(s(t_fun(TV_Q72295,TV_Q72291),V_g),s(TV_Q72295,V_x))) => s(t_fun(TV_Q72295,TV_Q72291),V_f) = s(t_fun(TV_Q72295,TV_Q72291),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_lists_LENGTHu_u_GENLIST, axiom, ![TV_u_27a]: ![V_n, V_f]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_listRanges_listRangeLHIu_u_def, axiom, ![V_uu_0]: (![V_m, V_i]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_i))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_i))) => ![V_n, V_m]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_listranges_listrangelhi(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))).
fof(ch4s_listRanges_LENGTHu_u_listRangeLHI, conjecture, ![V_lo, V_hi]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_nums_num),h4s_listranges_listrangelhi(s(t_h4s_nums_num,V_lo),s(t_h4s_nums_num,V_hi))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_hi),s(t_h4s_nums_num,V_lo)))).
