%   ORIGINAL: h4/quotient/RESPECTS__o
% 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/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/quotient/RESPECTS__THM: !f R2 R1. h4/quotient/respects (h4/quotient/_3D_3D_3D_3E R1 R2) f <=> (!x y. R1 x y ==> R2 (f x) (f y))
% Goal: !g f R3 R2 R1. h4/quotient/respects (h4/quotient/_3D_3D_3D_3E R2 R3) f /\ h4/quotient/respects (h4/quotient/_3D_3D_3D_3E R1 R2) g ==> h4/quotient/respects (h4/quotient/_3D_3D_3D_3E R1 R3) (h4/combin/o f g)
%   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_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_quotients_RESPECTSu_u_THM]: !f R2 R1. h4/quotient/respects (h4/quotient/_3D_3D_3D_3E R1 R2) f <=> (!x y. happ (happ R1 x) y ==> happ (happ R2 (happ f x)) (happ f y))
% Goal: !g f R3 R2 R1. h4/quotient/respects (h4/quotient/_3D_3D_3D_3E R2 R3) f /\ h4/quotient/respects (h4/quotient/_3D_3D_3D_3E R1 R2) g ==> h4/quotient/respects (h4/quotient/_3D_3D_3D_3E R1 R3) (h4/combin/o f g)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q224983,TV_Q224979]: ![V_f, V_g]: (![V_x]: s(TV_Q224979,happ(s(t_fun(TV_Q224983,TV_Q224979),V_f),s(TV_Q224983,V_x))) = s(TV_Q224979,happ(s(t_fun(TV_Q224983,TV_Q224979),V_g),s(TV_Q224983,V_x))) => s(t_fun(TV_Q224983,TV_Q224979),V_f) = s(t_fun(TV_Q224983,TV_Q224979),V_g))).
fof(ah4s_combins_ou_u_THM, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_x, V_g, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27c,TV_u_27a),V_g))),s(TV_u_27c,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),V_g),s(TV_u_27c,V_x)))))).
fof(ah4s_quotients_RESPECTSu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R2, V_R1]: (p(s(t_bool,h4s_quotients_respects(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(t_fun(TV_u_27a,TV_u_27b),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R1),s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2))),s(t_fun(TV_u_27a,TV_u_27b),V_f)))) <=> ![V_x, V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R1),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))) => p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))))))))).
fof(ch4s_quotients_RESPECTSu_u_o, conjecture, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_g, V_f, V_R3, V_R2, V_R1]: ((p(s(t_bool,h4s_quotients_respects(s(t_fun(t_fun(TV_u_27b,TV_u_27c),t_fun(t_fun(TV_u_27b,TV_u_27c),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2),s(t_fun(TV_u_27c,t_fun(TV_u_27c,t_bool)),V_R3))),s(t_fun(TV_u_27b,TV_u_27c),V_f)))) & p(s(t_bool,h4s_quotients_respects(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(t_fun(TV_u_27a,TV_u_27b),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R1),s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2))),s(t_fun(TV_u_27a,TV_u_27b),V_g))))) => p(s(t_bool,h4s_quotients_respects(s(t_fun(t_fun(TV_u_27a,TV_u_27c),t_fun(t_fun(TV_u_27a,TV_u_27c),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R1),s(t_fun(TV_u_27c,t_fun(TV_u_27c,t_bool)),V_R3))),s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_o(s(t_fun(TV_u_27b,TV_u_27c),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g)))))))).
