%   ORIGINAL: h4/set__relation/reln__rel__conv__thms_c12
% 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/set__relation/rcomp__to__rel__conv: !r2 r1. h4/set__relation/rcomp r1 r2 = h4/set__relation/rel__to__reln (h4/relation/O (h4/set__relation/reln__to__rel r2) (h4/set__relation/reln__to__rel r1))
% Goal: !r2 r1. h4/set__relation/rcomp r1 r2 = h4/set__relation/rel__to__reln (h4/relation/O (h4/set__relation/reln__to__rel r2) (h4/set__relation/reln__to__rel r1))
%   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_setu_u_relations_rcompu_u_tou_u_relu_u_conv]: !r2 r1. h4/set__relation/rcomp r1 r2 = h4/set__relation/rel__to__reln (h4/relation/O (h4/set__relation/reln__to__rel r2) (h4/set__relation/reln__to__rel r1))
% Goal: !r2 r1. h4/set__relation/rcomp r1 r2 = h4/set__relation/rel__to__reln (h4/relation/O (h4/set__relation/reln__to__rel r2) (h4/set__relation/reln__to__rel r1))
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_Q140076,TV_Q140072]: ![V_f, V_g]: (![V_x]: s(TV_Q140072,happ(s(t_fun(TV_Q140076,TV_Q140072),V_f),s(TV_Q140076,V_x))) = s(TV_Q140072,happ(s(t_fun(TV_Q140076,TV_Q140072),V_g),s(TV_Q140076,V_x))) => s(t_fun(TV_Q140076,TV_Q140072),V_f) = s(t_fun(TV_Q140076,TV_Q140072),V_g))).
fof(ah4s_setu_u_relations_rcompu_u_tou_u_relu_u_conv, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_r2, V_r1]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_setu_u_relations_rcomp(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),V_r1),s(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),V_r2))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_setu_u_relations_relu_u_tou_u_reln(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),h4s_relations_o(s(t_fun(TV_u_27c,t_fun(TV_u_27b,t_bool)),h4s_setu_u_relations_relnu_u_tou_u_rel(s(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),V_r2))),s(t_fun(TV_u_27a,t_fun(TV_u_27c,t_bool)),h4s_setu_u_relations_relnu_u_tou_u_rel(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),V_r1)))))))).
fof(ch4s_setu_u_relations_relnu_u_relu_u_convu_u_thmsu_c12, conjecture, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_r2, V_r1]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_setu_u_relations_rcomp(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),V_r1),s(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),V_r2))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_setu_u_relations_relu_u_tou_u_reln(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),h4s_relations_o(s(t_fun(TV_u_27c,t_fun(TV_u_27b,t_bool)),h4s_setu_u_relations_relnu_u_tou_u_rel(s(t_fun(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),t_bool),V_r2))),s(t_fun(TV_u_27a,t_fun(TV_u_27c,t_bool)),h4s_setu_u_relations_relnu_u_tou_u_rel(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27c),t_bool),V_r1)))))))).
