%   ORIGINAL: h4/set__relation/irreflexive__reln__to__rel__conv__UNIV
% 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/set__relation/REL__RESTRICT__UNIV: !R. h4/pred__set/REL__RESTRICT R h4/pred__set/UNIV = R
% Assm: h4/set__relation/irreflexive__reln__to__rel__conv: !s r. h4/set__relation/irreflexive r s <=> h4/relation/irreflexive (h4/pred__set/REL__RESTRICT (h4/set__relation/reln__to__rel r) s)
% Goal: !r. h4/set__relation/irreflexive r h4/pred__set/UNIV <=> h4/relation/irreflexive (h4/set__relation/reln__to__rel r)
%   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_setu_u_relations_RELu_u_RESTRICTu_u_UNIV]: !R. h4/pred__set/REL__RESTRICT R h4/pred__set/UNIV = R
% Assm [h4s_setu_u_relations_irreflexiveu_u_relnu_u_tou_u_relu_u_conv]: !s r. h4/set__relation/irreflexive r s <=> h4/relation/irreflexive (h4/pred__set/REL__RESTRICT (h4/set__relation/reln__to__rel r) s)
% Goal: !r. h4/set__relation/irreflexive r h4/pred__set/UNIV <=> h4/relation/irreflexive (h4/set__relation/reln__to__rel r)
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_Q139549,TV_Q139545]: ![V_f, V_g]: (![V_x]: s(TV_Q139545,happ(s(t_fun(TV_Q139549,TV_Q139545),V_f),s(TV_Q139549,V_x))) = s(TV_Q139545,happ(s(t_fun(TV_Q139549,TV_Q139545),V_g),s(TV_Q139549,V_x))) => s(t_fun(TV_Q139549,TV_Q139545),V_f) = s(t_fun(TV_Q139549,TV_Q139545),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_setu_u_relations_RELu_u_RESTRICTu_u_UNIV, axiom, ![TV_u_27a]: ![V_R]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_predu_u_sets_relu_u_restrict(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)).
fof(ah4s_setu_u_relations_irreflexiveu_u_relnu_u_tou_u_relu_u_conv, axiom, ![TV_u_27a]: ![V_s, V_r]: s(t_bool,h4s_setu_u_relations_irreflexive(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),t_bool),V_r),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_bool,h4s_relations_irreflexive(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_predu_u_sets_relu_u_restrict(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_setu_u_relations_relnu_u_tou_u_rel(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),t_bool),V_r))),s(t_fun(TV_u_27a,t_bool),V_s)))))).
fof(ch4s_setu_u_relations_irreflexiveu_u_relnu_u_tou_u_relu_u_convu_u_UNIV, conjecture, ![TV_u_27a]: ![V_r]: s(t_bool,h4s_setu_u_relations_irreflexive(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),t_bool),V_r),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ))) = s(t_bool,h4s_relations_irreflexive(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_setu_u_relations_relnu_u_tou_u_rel(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),t_bool),V_r)))))).
