%   ORIGINAL: h4/quotient__pred__set/FINITER__RSP
% 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/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/quotient__pred__set/FINITER__EQ: !s2 s1 R. h4/quotient/_3D_3D_3D_3E R $equals s1 s2 ==> (h4/quotient__pred__set/FINITER R s1 <=> h4/quotient__pred__set/FINITER R s2)
% Goal: !rep abs R. h4/quotient/QUOTIENT R abs rep ==> (!s1 s2. h4/quotient/_3D_3D_3D_3E R $equals s1 s2 ==> (h4/quotient__pred__set/FINITER R s1 <=> h4/quotient__pred__set/FINITER R s2))
%   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_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_quotientu_u_predu_u_sets_FINITERu_u_EQ]: !s2 s1 R. h4/quotient/_3D_3D_3D_3E R $equals s1 s2 ==> (h4/quotient__pred__set/FINITER R s1 <=> h4/quotient__pred__set/FINITER R s2)
% Goal: !rep abs R. h4/quotient/QUOTIENT R abs rep ==> (!s1 s2. h4/quotient/_3D_3D_3D_3E R $equals s1 s2 ==> (h4/quotient__pred__set/FINITER R s1 <=> h4/quotient__pred__set/FINITER R s2))
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_Q86328,TV_Q86324]: ![V_f, V_g]: (![V_x]: s(TV_Q86324,happ(s(t_fun(TV_Q86328,TV_Q86324),V_f),s(TV_Q86328,V_x))) = s(TV_Q86324,happ(s(t_fun(TV_Q86328,TV_Q86324),V_g),s(TV_Q86328,V_x))) => s(t_fun(TV_Q86328,TV_Q86324),V_f) = s(t_fun(TV_Q86328,TV_Q86324),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_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,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_quotientu_u_predu_u_sets_FINITERu_u_EQ, axiom, ![TV_u_27a]: ![V_s2, V_s1, V_R]: (p(s(t_bool,h4s_quotients_u_3du_3du_3du_3e(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_equals),s(t_fun(TV_u_27a,t_bool),V_s1),s(t_fun(TV_u_27a,t_bool),V_s2)))) => s(t_bool,h4s_quotientu_u_predu_u_sets_finiter(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),V_s1))) = s(t_bool,h4s_quotientu_u_predu_u_sets_finiter(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),V_s2))))).
fof(ch4s_quotientu_u_predu_u_sets_FINITERu_u_RSP, conjecture, ![TV_u_27b,TV_u_27a]: ![V_rep, V_abs, V_R]: (p(s(t_bool,h4s_quotients_quotient(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(t_fun(TV_u_27b,TV_u_27a),V_rep)))) => ![V_s1, V_s2]: (p(s(t_bool,h4s_quotients_u_3du_3du_3du_3e(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_equals),s(t_fun(TV_u_27a,t_bool),V_s1),s(t_fun(TV_u_27a,t_bool),V_s2)))) => s(t_bool,h4s_quotientu_u_predu_u_sets_finiter(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),V_s1))) = s(t_bool,h4s_quotientu_u_predu_u_sets_finiter(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),V_s2)))))).
