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Proofgold Asset

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0082279a6e576ef7906fc22eeace073a4b027571558d12788f3a32d5a61559af
asset hash
8577cfeacd0a27ac057daedaa3d0144d8098f2edb16ba417860e0c97bc4ecaed
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9725
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118eb..
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doc published by PrCx1..
Param lam_idlam_id : ιι
Param apap : ιιι
Definition struct_idstruct_id := λ x0 . lam_id (ap x0 0)
Param lam_complam_comp : ιιιι
Definition struct_compstruct_comp := λ x0 x1 x2 . lam_comp (ap x0 0)
Definition andand := λ x0 x1 : ο . ∀ x2 : ο . (x0x1x2)x2
Param struct_rstruct_r : ιο
Param unpack_r_ounpack_r_o : ι(ι(ιιο) → ο) → ο
Param notnot : οο
Param oror : οοο
Definition 8b17e..struct_r_wellord := λ x0 . and (struct_r x0) (unpack_r_o x0 (λ x1 . λ x2 : ι → ι → ο . and (and (and (∀ x3 . x3x1not (x2 x3 x3)) (∀ x3 . x3x1∀ x4 . x4x1or (x2 x3 x4) (x2 x4 x3))) (∀ x3 . x3x1∀ x4 . x4x1∀ x5 . x5x1x2 x3 x4x2 x4 x5x2 x3 x5)) (∀ x3 : ι → ο . (∀ x4 . x4x1(∀ x5 . x5x1x2 x5 x4x3 x5)x3 x4)∀ x4 . x4x1x3 x4)))
Param MetaCatMetaCat : (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → ο
Param BinRelnHomHom_struct_r : ιιιο
Known 62658..MetaCat_struct_r_gen : ∀ x0 : ι → ο . (∀ x1 . x0 x1struct_r x1)MetaCat x0 BinRelnHom (λ x1 . lam_id (ap x1 0)) (λ x1 x2 x3 . lam_comp (ap x1 0))
Theorem 85435..MetaCat_struct_r_wellord : MetaCat 8b17e.. BinRelnHom struct_id struct_comp (proof)
Param MetaFunctorMetaFunctor : (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → (ιι) → (ιιιι) → ο
Param TrueTrue : ο
Param HomSetSetHom : ιιιο
Known 45945..MetaCat_struct_r_Forgetful_gen : ∀ x0 : ι → ο . (∀ x1 . x0 x1struct_r x1)MetaFunctor x0 BinRelnHom (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)
Theorem 3315e..MetaCat_struct_r_wellord_Forgetful : MetaFunctor 8b17e.. BinRelnHom struct_id struct_comp (λ x0 . True) HomSet lam_id (λ x0 x1 x2 . lam_comp x0) (λ x0 . ap x0 0) (λ x0 x1 x2 . x2) (proof)
Param MetaCat_initial_pinitial_p : (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → ι(ιι) → ο
Conjecture 105dd..MetaCat_struct_r_wellord_initial : ∀ x0 : ο . (∀ x1 . (∀ x2 : ο . (∀ x3 : ι → ι . MetaCat_initial_p 8b17e.. BinRelnHom struct_id struct_comp x1 x3x2)x2)x0)x0
Param MetaCat_terminal_pterminal_p : (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → ι(ιι) → ο
Conjecture 49763..MetaCat_struct_r_wellord_terminal : ∀ x0 : ο . (∀ x1 . (∀ x2 : ο . (∀ x3 : ι → ι . MetaCat_terminal_p 8b17e.. BinRelnHom struct_id struct_comp x1 x3x2)x2)x0)x0
Param MetaCat_coproduct_constr_pcoproduct_constr_p : (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → (ιιι) → (ιιι) → (ιιι) → (ιιιιιι) → ο
Conjecture 17458..MetaCat_struct_r_wellord_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 8b17e.. BinRelnHom struct_id struct_comp x1 x3 x5 x7x6)x6)x4)x4)x2)x2)x0)x0
Param MetaCat_product_constr_pproduct_constr_p : (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → (ιιι) → (ιιι) → (ιιι) → (ιιιιιι) → ο
Conjecture 71d59..MetaCat_struct_r_wellord_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 8b17e.. BinRelnHom struct_id struct_comp x1 x3 x5 x7x6)x6)x4)x4)x2)x2)x0)x0
Param MetaCat_coequalizer_buggy_struct_p : (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → (ιιιιι) → (ιιιιι) → (ιιιιιιι) → ο
Conjecture 69725.. : ∀ 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 8b17e.. BinRelnHom struct_id struct_comp x1 x3 x5x4)x4)x2)x2)x0)x0
Param MetaCat_equalizer_buggy_struct_p : (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → (ιιιιι) → (ιιιιι) → (ιιιιιιι) → ο
Conjecture d6008.. : ∀ 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 8b17e.. BinRelnHom struct_id struct_comp x1 x3 x5x4)x4)x2)x2)x0)x0
Param MetaCat_pushout_buggy_constr_p : (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → (ιιιιιι) → (ιιιιιι) → (ιιιιιι) → (ιιιιιιιιι) → ο
Conjecture d3e44.. : ∀ 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 8b17e.. BinRelnHom struct_id struct_comp x1 x3 x5 x7x6)x6)x4)x4)x2)x2)x0)x0
Param MetaCat_pullback_buggy_struct_p : (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → (ιιιιιι) → (ιιιιιι) → (ιιιιιι) → (ιιιιιιιιι) → ο
Conjecture 4916b.. : ∀ 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 8b17e.. BinRelnHom struct_id struct_comp x1 x3 x5 x7x6)x6)x4)x4)x2)x2)x0)x0
Param MetaCat_exp_constr_pproduct_exponent_constr_p : (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → (ιιι) → (ιιι) → (ιιι) → (ιιιιιι) → (ιιι) → (ιιι) → (ιιιιι) → ο
Conjecture 9460d..MetaCat_struct_r_wellord_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 8b17e.. BinRelnHom struct_id struct_comp x1 x3 x5 x7 x9 x11 x13x12)x12)x10)x10)x8)x8)x6)x6)x4)x4)x2)x2)x0)x0
Param MetaCat_subobject_classifier_buggy_p : (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → ι(ιι) → ιι(ιιιι) → (ιιιιιιι) → ο
Conjecture 1e983.. : ∀ 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 8b17e.. BinRelnHom struct_id struct_comp x1 x3 x5 x7 x9 x11x10)x10)x8)x8)x6)x6)x4)x4)x2)x2)x0)x0
Param MetaCat_nno_pnno_p : (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → ι(ιι) → ιιι(ιιιι) → ο
Conjecture d6d09..MetaCat_struct_r_wellord_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 8b17e.. BinRelnHom struct_id struct_comp x1 x3 x5 x7 x9 x11x10)x10)x8)x8)x6)x6)x4)x4)x2)x2)x0)x0
Param MetaAdjunction_strictMetaAdjunction_strict : (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → (ιο) → (ιιιο) → (ιι) → (ιιιιιι) → (ιι) → (ιιιι) → (ιι) → (ιιιι) → (ιι) → (ιι) → ο
Conjecture 538f6..MetaCat_struct_r_wellord_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) 8b17e.. BinRelnHom struct_id struct_comp x1 x3 (λ x8 . ap x8 0) (λ x8 x9 x10 . x10) x5 x7x6)x6)x4)x4)x2)x2)x0)x0