%   ORIGINAL: h4/quote/compare__list__index
% 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/prelim/compare__equal: !cmp. (!x y. cmp x y = h4/prelim/EQUAL <=> x = y) ==> (!l1 l2. h4/prelim/list__compare cmp l1 l2 = h4/prelim/EQUAL <=> l1 = l2)
% Assm: h4/quote/compare__index__equal: !i2 i1. h4/quote/index__compare i1 i2 = h4/prelim/EQUAL <=> i1 = i2
% Goal: !l2 l1. h4/prelim/list__compare h4/quote/index__compare l1 l2 = h4/prelim/EQUAL <=> l1 = l2
%   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_prelims_compareu_u_equal]: !cmp. (!x y. happ (happ cmp x) y = h4/prelim/EQUAL <=> x = y) ==> (!l1 l2. h4/prelim/list__compare cmp l1 l2 = h4/prelim/EQUAL <=> l1 = l2)
% Assm [h4s_quotes_compareu_u_indexu_u_equal]: !i2 i1. happ (happ h4/quote/index__compare i1) i2 = h4/prelim/EQUAL <=> i1 = i2
% Goal: !l2 l1. h4/prelim/list__compare h4/quote/index__compare l1 l2 = h4/prelim/EQUAL <=> l1 = l2
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_Q344931,TV_Q344927]: ![V_f, V_g]: (![V_x]: s(TV_Q344927,happ(s(t_fun(TV_Q344931,TV_Q344927),V_f),s(TV_Q344931,V_x))) = s(TV_Q344927,happ(s(t_fun(TV_Q344931,TV_Q344927),V_g),s(TV_Q344931,V_x))) => s(t_fun(TV_Q344931,TV_Q344927),V_f) = s(t_fun(TV_Q344931,TV_Q344927),V_g))).
fof(ah4s_prelims_compareu_u_equal, axiom, ![TV_u_27a]: ![V_cmp]: (![V_x, V_y]: (s(t_h4s_prelims_ordering,happ(s(t_fun(TV_u_27a,t_h4s_prelims_ordering),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_prelims_ordering)),V_cmp),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))) = s(t_h4s_prelims_ordering,h4s_prelims_equal) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y)) => ![V_l1, V_l2]: (s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_prelims_ordering)),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_prelims_ordering,h4s_prelims_equal) <=> s(t_h4s_lists_list(TV_u_27a),V_l1) = s(t_h4s_lists_list(TV_u_27a),V_l2)))).
fof(ah4s_quotes_compareu_u_indexu_u_equal, axiom, ![V_i2, V_i1]: (s(t_h4s_prelims_ordering,happ(s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_quotes_index,V_i1))),s(t_h4s_quotes_index,V_i2))) = s(t_h4s_prelims_ordering,h4s_prelims_equal) <=> s(t_h4s_quotes_index,V_i1) = s(t_h4s_quotes_index,V_i2))).
fof(ch4s_quotes_compareu_u_listu_u_index, conjecture, ![V_l2, V_l1]: (s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))) = s(t_h4s_prelims_ordering,h4s_prelims_equal) <=> s(t_h4s_lists_list(t_h4s_quotes_index),V_l1) = s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))).
