%   ORIGINAL: h4/integerRing/int__ring__thms_c8
% 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/quote/varmap__find__def_c0: !x v2 v1. h4/quote/varmap__find h4/quote/End__idx (h4/quote/Node__vm x v1 v2) = x
% Assm: h4/quote/varmap__find__def_c1: !x v2 v1 i1. h4/quote/varmap__find (h4/quote/Right__idx i1) (h4/quote/Node__vm x v1 v2) = h4/quote/varmap__find i1 v2
% Assm: h4/quote/varmap__find__def_c2: !x v2 v1 i1. h4/quote/varmap__find (h4/quote/Left__idx i1) (h4/quote/Node__vm x v1 v2) = h4/quote/varmap__find i1 v1
% Assm: h4/quote/varmap__find__def_c3: !i. h4/quote/varmap__find i h4/quote/Empty__vm = h4/min/_40 (\x. T)
% Goal: !x v2 v1 i1. h4/quote/varmap__find (h4/quote/Right__idx i1) (h4/quote/Node__vm x v1 v2) = h4/quote/varmap__find i1 v2
%   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_quotes_varmapu_u_findu_u_defu_c0]: !x v2 v1. h4/quote/varmap__find h4/quote/End__idx (h4/quote/Node__vm x v1 v2) = x
% Assm [h4s_quotes_varmapu_u_findu_u_defu_c1]: !x v2 v1 i1. h4/quote/varmap__find (h4/quote/Right__idx i1) (h4/quote/Node__vm x v1 v2) = h4/quote/varmap__find i1 v2
% Assm [h4s_quotes_varmapu_u_findu_u_defu_c2]: !x v2 v1 i1. h4/quote/varmap__find (h4/quote/Left__idx i1) (h4/quote/Node__vm x v1 v2) = h4/quote/varmap__find i1 v1
% Assm [h4s_quotes_varmapu_u_findu_u_defu_c3]: !_0. (!x. happ _0 x <=> T) ==> (!i. h4/quote/varmap__find i h4/quote/Empty__vm = h4/min/_40 _0)
% Goal: !x v2 v1 i1. h4/quote/varmap__find (h4/quote/Right__idx i1) (h4/quote/Node__vm x v1 v2) = h4/quote/varmap__find i1 v2
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_Q165998,TV_Q165994]: ![V_f, V_g]: (![V_x]: s(TV_Q165994,happ(s(t_fun(TV_Q165998,TV_Q165994),V_f),s(TV_Q165998,V_x))) = s(TV_Q165994,happ(s(t_fun(TV_Q165998,TV_Q165994),V_g),s(TV_Q165998,V_x))) => s(t_fun(TV_Q165998,TV_Q165994),V_f) = s(t_fun(TV_Q165998,TV_Q165994),V_g))).
fof(ah4s_quotes_varmapu_u_findu_u_defu_c0, axiom, ![TV_u_27a]: ![V_x, V_v2, V_v1]: s(TV_u_27a,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,h4s_quotes_endu_u_idx),s(t_h4s_quotes_varmap(TV_u_27a),h4s_quotes_nodeu_u_vm(s(TV_u_27a,V_x),s(t_h4s_quotes_varmap(TV_u_27a),V_v1),s(t_h4s_quotes_varmap(TV_u_27a),V_v2))))) = s(TV_u_27a,V_x)).
fof(ah4s_quotes_varmapu_u_findu_u_defu_c1, axiom, ![TV_u_27a]: ![V_x, V_v2, V_v1, V_i1]: s(TV_u_27a,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,h4s_quotes_rightu_u_idx(s(t_h4s_quotes_index,V_i1))),s(t_h4s_quotes_varmap(TV_u_27a),h4s_quotes_nodeu_u_vm(s(TV_u_27a,V_x),s(t_h4s_quotes_varmap(TV_u_27a),V_v1),s(t_h4s_quotes_varmap(TV_u_27a),V_v2))))) = s(TV_u_27a,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,V_i1),s(t_h4s_quotes_varmap(TV_u_27a),V_v2)))).
fof(ah4s_quotes_varmapu_u_findu_u_defu_c2, axiom, ![TV_u_27a]: ![V_x, V_v2, V_v1, V_i1]: s(TV_u_27a,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,h4s_quotes_leftu_u_idx(s(t_h4s_quotes_index,V_i1))),s(t_h4s_quotes_varmap(TV_u_27a),h4s_quotes_nodeu_u_vm(s(TV_u_27a,V_x),s(t_h4s_quotes_varmap(TV_u_27a),V_v1),s(t_h4s_quotes_varmap(TV_u_27a),V_v2))))) = s(TV_u_27a,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,V_i1),s(t_h4s_quotes_varmap(TV_u_27a),V_v1)))).
fof(ah4s_quotes_varmapu_u_findu_u_defu_c3, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_x]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_uu_0),s(TV_u_27a,V_x))) = s(t_bool,t) => ![V_i]: s(TV_u_27a,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,V_i),s(t_h4s_quotes_varmap(TV_u_27a),h4s_quotes_emptyu_u_vm))) = s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_uu_0))))).
fof(ch4s_integerRings_intu_u_ringu_u_thmsu_c8, conjecture, ![TV_u_27a]: ![V_x, V_v2, V_v1, V_i1]: s(TV_u_27a,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,h4s_quotes_rightu_u_idx(s(t_h4s_quotes_index,V_i1))),s(t_h4s_quotes_varmap(TV_u_27a),h4s_quotes_nodeu_u_vm(s(TV_u_27a,V_x),s(t_h4s_quotes_varmap(TV_u_27a),V_v1),s(t_h4s_quotes_varmap(TV_u_27a),V_v2))))) = s(TV_u_27a,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,V_i1),s(t_h4s_quotes_varmap(TV_u_27a),V_v2)))).
