%   ORIGINAL: h4/bitstring/ops__to__v2w_c10
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bitstring/v2w__n2v: !n. h4/bitstring/v2w (h4/bitstring/n2v n) = h4/words/n2w n
% Goal: !v n. h4/words/word__xnor (h4/bitstring/v2w v) (h4/words/n2w n) = h4/words/word__xnor (h4/bitstring/v2w v) (h4/bitstring/v2w (h4/bitstring/n2v 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_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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bitstrings_v2wu_u_n2v]: !n. h4/bitstring/v2w (h4/bitstring/n2v n) = h4/words/n2w n
% Goal: !v n. h4/words/word__xnor (h4/bitstring/v2w v) (h4/words/n2w n) = h4/words/word__xnor (h4/bitstring/v2w v) (h4/bitstring/v2w (h4/bitstring/n2v 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_Q90037,TV_Q90033]: ![V_f, V_g]: (![V_x]: s(TV_Q90033,happ(s(t_fun(TV_Q90037,TV_Q90033),V_f),s(TV_Q90037,V_x))) = s(TV_Q90033,happ(s(t_fun(TV_Q90037,TV_Q90033),V_g),s(TV_Q90037,V_x))) => s(t_fun(TV_Q90037,TV_Q90033),V_f) = s(t_fun(TV_Q90037,TV_Q90033),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_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_bitstrings_v2wu_u_n2v, axiom, ![TV_u_27a]: ![V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),h4s_bitstrings_n2v(s(t_h4s_nums_num,V_n))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n)))).
fof(ch4s_bitstrings_opsu_u_tou_u_v2wu_c10, conjecture, ![TV_u_27m]: ![V_v, V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27m),h4s_wordss_wordu_u_xnor(s(t_h4s_fcps_cart(t_bool,TV_u_27m),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27m),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27m),h4s_wordss_wordu_u_xnor(s(t_h4s_fcps_cart(t_bool,TV_u_27m),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27m),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),h4s_bitstrings_n2v(s(t_h4s_nums_num,V_n)))))))).
