%   ORIGINAL: h4/bitstring/extend0_c0
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bitstring/zero__extend__def: !v n. h4/bitstring/zero__extend n v = h4/list/PAD__LEFT F n v
% Assm: h4/bitstring/sign__extend__def: !v n. h4/bitstring/sign__extend n v = h4/list/PAD__LEFT (h4/list/HD v) n v
% Assm: h4/bitstring/pad__left__extend: !n l c. h4/list/PAD__LEFT c n l = h4/bitstring/extend c (h4/arithmetic/_2D n (h4/list/LENGTH l)) l
% Goal: !v n. h4/bitstring/zero__extend n v = h4/bitstring/extend F (h4/arithmetic/_2D n (h4/list/LENGTH v)) v
%   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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bitstrings_zerou_u_extendu_u_def]: !v n. h4/bitstring/zero__extend n v = h4/list/PAD__LEFT F n v
% Assm [h4s_bitstrings_signu_u_extendu_u_def]: !v n. h4/bitstring/sign__extend n v = h4/list/PAD__LEFT (h4/list/HD v) n v
% Assm [h4s_bitstrings_padu_u_leftu_u_extend]: !n l c. h4/list/PAD__LEFT c n l = h4/bitstring/extend c (h4/arithmetic/_2D n (h4/list/LENGTH l)) l
% Goal: !v n. h4/bitstring/zero__extend n v = h4/bitstring/extend F (h4/arithmetic/_2D n (h4/list/LENGTH v)) v
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_Q87753,TV_Q87749]: ![V_f, V_g]: (![V_x]: s(TV_Q87749,happ(s(t_fun(TV_Q87753,TV_Q87749),V_f),s(TV_Q87753,V_x))) = s(TV_Q87749,happ(s(t_fun(TV_Q87753,TV_Q87749),V_g),s(TV_Q87753,V_x))) => s(t_fun(TV_Q87753,TV_Q87749),V_f) = s(t_fun(TV_Q87753,TV_Q87749),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bitstrings_zerou_u_extendu_u_def, axiom, ![V_v, V_n]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_zerou_u_extend(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_v))) = s(t_h4s_lists_list(t_bool),h4s_lists_padu_u_left(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_v)))).
fof(ah4s_bitstrings_signu_u_extendu_u_def, axiom, ![TV_u_27a]: ![V_v, V_n]: s(t_h4s_lists_list(TV_u_27a),h4s_bitstrings_signu_u_extend(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_v))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_padu_u_left(s(TV_u_27a,h4s_lists_hd(s(t_h4s_lists_list(TV_u_27a),V_v))),s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_v)))).
fof(ah4s_bitstrings_padu_u_leftu_u_extend, axiom, ![TV_u_27a]: ![V_n, V_l, V_c]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_padu_u_left(s(TV_u_27a,V_c),s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_bitstrings_extend(s(TV_u_27a,V_c),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))))),s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ch4s_bitstrings_extend0u_c0, conjecture, ![V_v, V_n]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_zerou_u_extend(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_v))) = s(t_h4s_lists_list(t_bool),h4s_bitstrings_extend(s(t_bool,f),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v))))),s(t_h4s_lists_list(t_bool),V_v)))).
