%   ORIGINAL: h4/sptree/lrnext__thm_c3
% 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/sptree/lrnext__def_c1: !n. h4/sptree/lrnext (h4/arithmetic/BIT1 n) = h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/sptree/lrnext n)
% Goal: !n. h4/sptree/lrnext (h4/arithmetic/BIT1 n) = h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/sptree/lrnext n)
%   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_sptrees_lrnextu_u_defu_c1]: !n. h4/sptree/lrnext (h4/arithmetic/BIT1 n) = h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/sptree/lrnext n)
% Goal: !n. h4/sptree/lrnext (h4/arithmetic/BIT1 n) = h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/sptree/lrnext n)
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_Q81894,TV_Q81890]: ![V_f, V_g]: (![V_x]: s(TV_Q81890,happ(s(t_fun(TV_Q81894,TV_Q81890),V_f),s(TV_Q81894,V_x))) = s(TV_Q81890,happ(s(t_fun(TV_Q81894,TV_Q81890),V_g),s(TV_Q81894,V_x))) => s(t_fun(TV_Q81894,TV_Q81890),V_f) = s(t_fun(TV_Q81894,TV_Q81890),V_g))).
fof(ah4s_sptrees_lrnextu_u_defu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_sptrees_lrnext(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_sptrees_lrnext(s(t_h4s_nums_num,V_n)))))).
fof(ch4s_sptrees_lrnextu_u_thmu_c3, conjecture, ![V_n]: s(t_h4s_nums_num,h4s_sptrees_lrnext(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_sptrees_lrnext(s(t_h4s_nums_num,V_n)))))).
