Proofgold Address

Param lam^Sigma : ι → (ι → ι) → ι
Definition lam_id^lam_id := λ x0 . lam x0 (λ x1 . x1)
Param ap^ap : ι → ι → ι
Definition struct_id^struct_id := λ x0 . lam_id (ap x0 0)
Definition lam_comp^lam_comp := λ x0 x1 x2 . lam x0 (λ x3 . ap x1 (ap x2 x3))
Definition struct_comp^struct_comp := λ x0 x1 x2 . lam_comp (ap x0 0)
Definition and^and := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2
Definition MetaCat_initial_p^initial_p := λ x0 : ι → ο . λ x1 : ι → ι → ι → ο . λ x2 : ι → ι . λ x3 : ι → ι → ι → ι → ι → ι . λ x4 . λ x5 : ι → ι . and (x0 x4) (∀ x6 . x0 x6 ⟶ and (x1 x4 x6 (x5 x6)) (∀ x7 . x1 x4 x6 x7 ⟶ x7 = x5 x6))
Param pack_e^pack_e : ι → ι → ι
Definition struct_e^struct_e := λ x0 . ∀ x1 : ι → ο . (∀ x2 x3 . x3 ∈ x2 ⟶ x1 (pack_e x2 x3)) ⟶ x1 x0
Param PtdSetHom^Hom_struct_e : ι → ι → ι → ο
Param ordsucc^ordsucc : ι → ι
Known andI^andI : ∀ x0 x1 : ο . x0 ⟶ x1 ⟶ and x0 x1
Known pack_struct_e_I^{pack_struct_e_I} : ∀ x0 x1 . x1 ∈ x0 ⟶ struct_e (pack_e x0 x1)
Known In_0_1^In_0_1 : 0 ∈ 1
Known pack_e_1_eq2^pack_e_1_eq2 : ∀ x0 x1 . x1 = ap (pack_e x0 x1) 1
Param Pi^Pi : ι → (ι → ι) → ι
Definition setexp^setexp := λ x0 x1 . Pi x1 (λ x2 . x0)
Known f65a3..^{Hom_struct_e_pack} : ∀ x0 x1 x2 x3 x4 . PtdSetHom (pack_e x0 x2) (pack_e x1 x3) x4 = and (x4 ∈ setexp x1 x0) (ap x4 x2 = x3)
Known lam_Pi^lam_Pi : ∀ x0 . ∀ x1 x2 : ι → ι . (∀ x3 . x3 ∈ x0 ⟶ x2 x3 ∈ x1 x3) ⟶ lam x0 x2 ∈ Pi x0 x1
Known beta^beta : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . x2 ∈ x0 ⟶ ap (lam x0 x1) x2 = x1 x2
Known Pi_eta^Pi_eta : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . x2 ∈ Pi x0 x1 ⟶ lam x0 (ap x2) = x2
Known encode_u_ext^encode_u_ext : ∀ x0 . ∀ x1 x2 : ι → ι . (∀ x3 . x3 ∈ x0 ⟶ x1 x3 = x2 x3) ⟶ lam x0 x1 = lam x0 x2
Known cases_1^cases_1 : ∀ x0 . x0 ∈ 1 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 x0
Theorem 11b66..^{MetaCat_struct_e_initial} : ∀ x0 : ο . (∀ x1 . (∀ x2 : ο . (∀ x3 : ι → ι . MetaCat_initial_p struct_e PtdSetHom struct_id struct_comp x1 x3 ⟶ x2) ⟶ x2) ⟶ x0) ⟶ x0 (proof)
Param MetaCat_terminal_p^terminal_p : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → ι → (ι → ι) → ο
Conjecture b5447..^{MetaCat_struct_e_terminal} : ∀ x0 : ο . (∀ x1 . (∀ x2 : ο . (∀ x3 : ι → ι . MetaCat_terminal_p struct_e PtdSetHom struct_id struct_comp x1 x3 ⟶ x2) ⟶ x2) ⟶ x0) ⟶ x0
Param MetaCat_coproduct_constr_p^{coproduct_constr_p} : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι → ι → ι → ι) → ο
Conjecture 8da75..^{MetaCat_struct_e_coproduct_constr} : ∀ x0 : ο . (∀ x1 : ι → ι → ι . (∀ x2 : ο . (∀ x3 : ι → ι → ι . (∀ x4 : ο . (∀ x5 : ι → ι → ι . (∀ x6 : ο . (∀ x7 : ι → ι → ι → ι → ι → ι . MetaCat_coproduct_constr_p struct_e PtdSetHom struct_id struct_comp x1 x3 x5 x7 ⟶ x6) ⟶ x6) ⟶ x4) ⟶ x4) ⟶ x2) ⟶ x2) ⟶ x0) ⟶ x0
Param MetaCat_product_constr_p^{product_constr_p} : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι → ι → ι → ι) → ο
Conjecture 8e8d1..^{MetaCat_struct_e_product_constr} : ∀ x0 : ο . (∀ x1 : ι → ι → ι . (∀ x2 : ο . (∀ x3 : ι → ι → ι . (∀ x4 : ο . (∀ x5 : ι → ι → ι . (∀ x6 : ο . (∀ x7 : ι → ι → ι → ι → ι → ι . MetaCat_product_constr_p struct_e PtdSetHom struct_id struct_comp x1 x3 x5 x7 ⟶ x6) ⟶ x6) ⟶ x4) ⟶ x4) ⟶ x2) ⟶ x2) ⟶ x0) ⟶ x0
Param MetaCat_coequalizer_buggy_struct_p : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι → ι → ι) → ο
Conjecture 8fa6b.. : ∀ x0 : ο . (∀ x1 : ι → ι → ι → ι → ι . (∀ x2 : ο . (∀ x3 : ι → ι → ι → ι → ι . (∀ x4 : ο . (∀ x5 : ι → ι → ι → ι → ι → ι → ι . MetaCat_coequalizer_buggy_struct_p struct_e PtdSetHom struct_id struct_comp x1 x3 x5 ⟶ x4) ⟶ x4) ⟶ x2) ⟶ x2) ⟶ x0) ⟶ x0
Param MetaCat_equalizer_buggy_struct_p : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι → ι → ι) → ο
Conjecture a9707.. : ∀ x0 : ο . (∀ x1 : ι → ι → ι → ι → ι . (∀ x2 : ο . (∀ x3 : ι → ι → ι → ι → ι . (∀ x4 : ο . (∀ x5 : ι → ι → ι → ι → ι → ι → ι . MetaCat_equalizer_buggy_struct_p struct_e PtdSetHom struct_id struct_comp x1 x3 x5 ⟶ x4) ⟶ x4) ⟶ x2) ⟶ x2) ⟶ x0) ⟶ x0
Param MetaCat_pushout_buggy_constr_p : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι → ι → ι → ι → ι) → ο
Conjecture a309a.. : ∀ x0 : ο . (∀ x1 : ι → ι → ι → ι → ι → ι . (∀ x2 : ο . (∀ x3 : ι → ι → ι → ι → ι → ι . (∀ x4 : ο . (∀ x5 : ι → ι → ι → ι → ι → ι . (∀ x6 : ο . (∀ x7 : ι → ι → ι → ι → ι → ι → ι → ι → ι . MetaCat_pushout_buggy_constr_p struct_e PtdSetHom struct_id struct_comp x1 x3 x5 x7 ⟶ x6) ⟶ x6) ⟶ x4) ⟶ x4) ⟶ x2) ⟶ x2) ⟶ x0) ⟶ x0
Param MetaCat_pullback_buggy_struct_p : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι → ι → ι → ι → ι) → ο
Conjecture 728ef.. : ∀ x0 : ο . (∀ x1 : ι → ι → ι → ι → ι → ι . (∀ x2 : ο . (∀ x3 : ι → ι → ι → ι → ι → ι . (∀ x4 : ο . (∀ x5 : ι → ι → ι → ι → ι → ι . (∀ x6 : ο . (∀ x7 : ι → ι → ι → ι → ι → ι → ι → ι → ι . MetaCat_pullback_buggy_struct_p struct_e PtdSetHom struct_id struct_comp x1 x3 x5 x7 ⟶ x6) ⟶ x6) ⟶ x4) ⟶ x4) ⟶ x2) ⟶ x2) ⟶ x0) ⟶ x0
Param MetaCat_exp_constr_p^{product_exponent_constr_p} : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι → ι → ι) → ο
Conjecture d6977..^{MetaCat_struct_e_product_exponent} : ∀ x0 : ο . (∀ x1 : ι → ι → ι . (∀ x2 : ο . (∀ x3 : ι → ι → ι . (∀ x4 : ο . (∀ x5 : ι → ι → ι . (∀ x6 : ο . (∀ x7 : ι → ι → ι → ι → ι → ι . (∀ x8 : ο . (∀ x9 : ι → ι → ι . (∀ x10 : ο . (∀ x11 : ι → ι → ι . (∀ x12 : ο . (∀ x13 : ι → ι → ι → ι → ι . MetaCat_exp_constr_p struct_e PtdSetHom struct_id struct_comp x1 x3 x5 x7 x9 x11 x13 ⟶ x12) ⟶ x12) ⟶ x10) ⟶ x10) ⟶ x8) ⟶ x8) ⟶ x6) ⟶ x6) ⟶ x4) ⟶ x4) ⟶ x2) ⟶ x2) ⟶ x0) ⟶ x0
Param MetaCat_subobject_classifier_buggy_p : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → ι → (ι → ι) → ι → ι → (ι → ι → ι → ι) → (ι → ι → ι → ι → ι → ι → ι) → ο
Conjecture 5a560.. : ∀ x0 : ο . (∀ x1 . (∀ x2 : ο . (∀ x3 : ι → ι . (∀ x4 : ο . (∀ x5 . (∀ x6 : ο . (∀ x7 . (∀ x8 : ο . (∀ x9 : ι → ι → ι → ι . (∀ x10 : ο . (∀ x11 : ι → ι → ι → ι → ι → ι → ι . MetaCat_subobject_classifier_buggy_p struct_e PtdSetHom struct_id struct_comp x1 x3 x5 x7 x9 x11 ⟶ x10) ⟶ x10) ⟶ x8) ⟶ x8) ⟶ x6) ⟶ x6) ⟶ x4) ⟶ x4) ⟶ x2) ⟶ x2) ⟶ x0) ⟶ x0
Param MetaCat_nno_p^nno_p : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → ι → (ι → ι) → ι → ι → ι → (ι → ι → ι → ι) → ο
Conjecture 99f2c..^{MetaCat_struct_e_nno} : ∀ x0 : ο . (∀ x1 . (∀ x2 : ο . (∀ x3 : ι → ι . (∀ x4 : ο . (∀ x5 . (∀ x6 : ο . (∀ x7 . (∀ x8 : ο . (∀ x9 . (∀ x10 : ο . (∀ x11 : ι → ι → ι → ι . MetaCat_nno_p struct_e PtdSetHom struct_id struct_comp x1 x3 x5 x7 x9 x11 ⟶ x10) ⟶ x10) ⟶ x8) ⟶ x8) ⟶ x6) ⟶ x6) ⟶ x4) ⟶ x4) ⟶ x2) ⟶ x2) ⟶ x0) ⟶ x0
Param MetaAdjunction_strict^{MetaAdjunction_strict} : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι) → (ι → ι → ι → ι) → (ι → ι) → (ι → ι → ι → ι) → (ι → ι) → (ι → ι) → ο
Param True^True : ο
Definition HomSet^SetHom := λ x0 x1 x2 . x2 ∈ setexp x1 x0
Param setsum^setsum : ι → ι → ι
Param combine_funcs^{combine_funcs} : ι → ι → (ι → ι) → (ι → ι) → ι → ι
Param Inj1^Inj1 : ι → ι
Param Inj0^Inj0 : ι → ι
Param MetaFunctor_strict^{MetaFunctor_strict} : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι) → (ι → ι → ι → ι) → ο
Param MetaFunctor^MetaFunctor : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι) → (ι → ι → ι → ι) → ο
Param MetaNatTrans^MetaNatTrans : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι) → (ι → ι → ι → ι) → (ι → ι) → (ι → ι → ι → ι) → (ι → ι) → ο
Param MetaAdjunction^{MetaAdjunction} : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → (ι → ι) → (ι → ι → ι → ι) → (ι → ι) → (ι → ι → ι → ι) → (ι → ι) → (ι → ι) → ο
Known d6aa5..^{MetaAdjunction_strict_I} : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ι → ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 : ι → ι → ι → ο . ∀ x6 : ι → ι . ∀ x7 : ι → ι → ι → ι → ι → ι . ∀ x8 : ι → ι . ∀ x9 : ι → ι → ι → ι . ∀ x10 : ι → ι . ∀ x11 : ι → ι → ι → ι . ∀ x12 x13 : ι → ι . MetaFunctor_strict x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ MetaFunctor x4 x5 x6 x7 x0 x1 x2 x3 x10 x11 ⟶ MetaNatTrans x0 x1 x2 x3 x0 x1 x2 x3 (λ x14 . x14) (λ x14 x15 x16 . x16) (λ x14 . x10 (x8 x14)) (λ x14 x15 x16 . x11 (x8 x14) (x8 x15) (x9 x14 x15 x16)) x12 ⟶ MetaNatTrans x4 x5 x6 x7 x4 x5 x6 x7 (λ x14 . x8 (x10 x14)) (λ x14 x15 x16 . x9 (x10 x14) (x10 x15) (x11 x14 x15 x16)) (λ x14 . x14) (λ x14 x15 x16 . x16) x13 ⟶ MetaAdjunction x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ MetaAdjunction_strict x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13
Param MetaCat^MetaCat : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → ο
Known 5cbb4..^{MetaFunctor_strict_I} : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ι → ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 : ι → ι → ι → ο . ∀ x6 : ι → ι . ∀ x7 : ι → ι → ι → ι → ι → ι . ∀ x8 : ι → ι . ∀ x9 : ι → ι → ι → ι . MetaCat x0 x1 x2 x3 ⟶ MetaCat x4 x5 x6 x7 ⟶ MetaFunctor x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ MetaFunctor_strict x0 x1 x2 x3 x4 x5 x6 x7 x8 x9
Known e4125..^MetaCatSet : MetaCat (λ x0 . True) HomSet lam_id (λ x0 x1 x2 . lam_comp x0)
Known 1c0e1..^{MetaCat_struct_e_gen} : ∀ x0 : ι → ο . (∀ x1 . x0 x1 ⟶ struct_e x1) ⟶ MetaCat x0 PtdSetHom (λ x1 . lam_id (ap x1 0)) (λ x1 x2 x3 . lam_comp (ap x1 0))
Known 2cb62..^MetaFunctorI : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ι → ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 : ι → ι → ι → ο . ∀ x6 : ι → ι . ∀ x7 : ι → ι → ι → ι → ι → ι . ∀ x8 : ι → ι . ∀ x9 : ι → ι → ι → ι . (∀ x10 . x0 x10 ⟶ x4 (x8 x10)) ⟶ (∀ x10 x11 x12 . x0 x10 ⟶ x0 x11 ⟶ x1 x10 x11 x12 ⟶ x5 (x8 x10) (x8 x11) (x9 x10 x11 x12)) ⟶ (∀ x10 . x0 x10 ⟶ x9 x10 x10 (x2 x10) = x6 (x8 x10)) ⟶ (∀ x10 x11 x12 x13 x14 . x0 x10 ⟶ x0 x11 ⟶ x0 x12 ⟶ x1 x10 x11 x13 ⟶ x1 x11 x12 x14 ⟶ x9 x10 x12 (x3 x10 x11 x12 x14 x13) = x7 (x8 x10) (x8 x11) (x8 x12) (x9 x11 x12 x14) (x9 x10 x11 x13)) ⟶ MetaFunctor x0 x1 x2 x3 x4 x5 x6 x7 x8 x9
Definition or^or := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x2) ⟶ (x1 ⟶ x2) ⟶ x2
Known setsum_Inj_inv^{setsum_Inj_inv} : ∀ x0 x1 x2 . x2 ∈ setsum x0 x1 ⟶ or (∀ x3 : ο . (∀ x4 . and (x4 ∈ x0) (x2 = Inj0 x4) ⟶ x3) ⟶ x3) (∀ x3 : ο . (∀ x4 . and (x4 ∈ x1) (x2 = Inj1 x4) ⟶ x3) ⟶ x3)
Known combine_funcs_eq1^{combine_funcs_eq1} : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 . combine_funcs x0 x1 x2 x3 (Inj0 x4) = x2 x4
Known Inj0_0^Inj0_0 : Inj0 0 = 0
Known combine_funcs_eq2^{combine_funcs_eq2} : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 . combine_funcs x0 x1 x2 x3 (Inj1 x4) = x3 x4
Known ap_Pi^ap_Pi : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 x3 . x2 ∈ Pi x0 x1 ⟶ x3 ∈ x0 ⟶ ap x2 x3 ∈ x1 x3
Known 0f4ef..^{MetaCat_struct_e_Forgetful_gen} : ∀ x0 : ι → ο . (∀ x1 . x0 x1 ⟶ struct_e x1) ⟶ MetaFunctor x0 PtdSetHom (λ x1 . lam_id (ap x1 0)) (λ x1 x2 x3 . lam_comp (ap x1 0)) (λ x1 . True) HomSet lam_id (λ x1 x2 x3 . lam_comp x1) (λ x1 . ap x1 0) (λ x1 x2 x3 . x3)
Known c1d68..^{MetaNatTransI} : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ι → ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 : ι → ι → ι → ο . ∀ x6 : ι → ι . ∀ x7 : ι → ι → ι → ι → ι → ι . ∀ x8 : ι → ι . ∀ x9 : ι → ι → ι → ι . ∀ x10 : ι → ι . ∀ x11 : ι → ι → ι → ι . ∀ x12 : ι → ι . (∀ x13 . x0 x13 ⟶ x5 (x8 x13) (x10 x13) (x12 x13)) ⟶ (∀ x13 x14 x15 . x0 x13 ⟶ x0 x14 ⟶ x1 x13 x14 x15 ⟶ x7 (x8 x13) (x10 x13) (x10 x14) (x11 x13 x14 x15) (x12 x13) = x7 (x8 x13) (x8 x14) (x10 x14) (x12 x14) (x9 x13 x14 x15)) ⟶ MetaNatTrans x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12
Known Inj1_setsum^Inj1_setsum : ∀ x0 x1 x2 . x2 ∈ x1 ⟶ Inj1 x2 ∈ setsum x0 x1
Known pack_e_0_eq2^pack_e_0_eq2 : ∀ x0 x1 . x0 = ap (pack_e x0 x1) 0
Known fd494..^{MetaAdjunctionI} : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ι → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ι → ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 : ι → ι → ι → ο . ∀ x6 : ι → ι . ∀ x7 : ι → ι → ι → ι → ι → ι . ∀ x8 : ι → ι . ∀ x9 : ι → ι → ι → ι . ∀ x10 : ι → ι . ∀ x11 : ι → ι → ι → ι . ∀ x12 x13 : ι → ι . (∀ x14 . x0 x14 ⟶ x7 (x8 x14) (x8 (x10 (x8 x14))) (x8 x14) (x13 (x8 x14)) (x9 x14 (x10 (x8 x14)) (x12 x14)) = x6 (x8 x14)) ⟶ (∀ x14 . x4 x14 ⟶ x3 (x10 x14) (x10 (x8 (x10 x14))) (x10 x14) (x11 (x8 (x10 x14)) x14 (x13 x14)) (x12 (x10 x14)) = x2 (x10 x14)) ⟶ MetaAdjunction x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13
Known Inj0_setsum^Inj0_setsum : ∀ x0 x1 x2 . x2 ∈ x0 ⟶ Inj0 x2 ∈ setsum x0 x1
Theorem 1ffb7..^{MetaCat_struct_e_left_adjoint_forgetful} : ∀ x0 : ο . (∀ x1 : ι → ι . (∀ x2 : ο . (∀ x3 : ι → ι → ι → ι . (∀ x4 : ο . (∀ x5 : ι → ι . (∀ x6 : ο . (∀ x7 : ι → ι . MetaAdjunction_strict (λ x8 . True) HomSet lam_id (λ x8 x9 x10 . lam_comp x8) struct_e PtdSetHom struct_id struct_comp x1 x3 (λ x8 . ap x8 0) (λ x8 x9 x10 . x10) x5 x7 ⟶ x6) ⟶ x6) ⟶ x4) ⟶ x4) ⟶ x2) ⟶ x2) ⟶ x0) ⟶ x0 (proof)