%   ORIGINAL: h4/finite__map/FMERGE__DOMSUB
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/finite__map/FMERGE__DRESTRICT: !vs st2 st1 f. h4/finite__map/DRESTRICT (h4/finite__map/FMERGE f st1 st2) vs = h4/finite__map/FMERGE f (h4/finite__map/DRESTRICT st1 vs) (h4/finite__map/DRESTRICT st2 vs)
% Assm: h4/finite__map/fmap__domsub: !k fm. h4/finite__map/fdomsub fm k = h4/finite__map/DRESTRICT fm (h4/pred__set/COMPL (h4/pred__set/INSERT k h4/pred__set/EMPTY))
% Goal: !m2 m1 m k. h4/finite__map/fdomsub (h4/finite__map/FMERGE m m1 m2) k = h4/finite__map/FMERGE m (h4/finite__map/fdomsub m1 k) (h4/finite__map/fdomsub m2 k)
%   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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_finiteu_u_maps_FMERGEu_u_DRESTRICT]: !vs st2 st1 f. h4/finite__map/DRESTRICT (h4/finite__map/FMERGE f st1 st2) vs = h4/finite__map/FMERGE f (h4/finite__map/DRESTRICT st1 vs) (h4/finite__map/DRESTRICT st2 vs)
% Assm [h4s_finiteu_u_maps_fmapu_u_domsub]: !k fm. h4/finite__map/fdomsub fm k = h4/finite__map/DRESTRICT fm (h4/pred__set/COMPL (h4/pred__set/INSERT k h4/pred__set/EMPTY))
% Goal: !m2 m1 m k. h4/finite__map/fdomsub (h4/finite__map/FMERGE m m1 m2) k = h4/finite__map/FMERGE m (h4/finite__map/fdomsub m1 k) (h4/finite__map/fdomsub m2 k)
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_Q75501,TV_Q75497]: ![V_f, V_g]: (![V_x]: s(TV_Q75497,happ(s(t_fun(TV_Q75501,TV_Q75497),V_f),s(TV_Q75501,V_x))) = s(TV_Q75497,happ(s(t_fun(TV_Q75501,TV_Q75497),V_g),s(TV_Q75501,V_x))) => s(t_fun(TV_Q75501,TV_Q75497),V_f) = s(t_fun(TV_Q75501,TV_Q75497),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_finiteu_u_maps_FMERGEu_u_DRESTRICT, axiom, ![TV_u_27b,TV_u_27a]: ![V_vs, V_st2, V_st1, V_f]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_fmerge(s(t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b)),V_f),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_st1),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_st2))),s(t_fun(TV_u_27a,t_bool),V_vs))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_fmerge(s(t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b)),V_f),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_st1),s(t_fun(TV_u_27a,t_bool),V_vs))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_st2),s(t_fun(TV_u_27a,t_bool),V_vs)))))).
fof(ah4s_finiteu_u_maps_fmapu_u_domsub, axiom, ![TV_u_27b,TV_u_27a]: ![V_k, V_fm]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_fdomsub(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_fm),s(TV_u_27a,V_k))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_fm),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_compl(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_k),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))))).
fof(ch4s_finiteu_u_maps_FMERGEu_u_DOMSUB, conjecture, ![TV_u_27a,TV_u_27b]: ![V_m2, V_m1, V_m, V_k]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),h4s_finiteu_u_maps_fdomsub(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),h4s_finiteu_u_maps_fmerge(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_m),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),V_m1),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),V_m2))),s(TV_u_27b,V_k))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),h4s_finiteu_u_maps_fmerge(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_m),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),h4s_finiteu_u_maps_fdomsub(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),V_m1),s(TV_u_27b,V_k))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),h4s_finiteu_u_maps_fdomsub(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),V_m2),s(TV_u_27b,V_k)))))).
