Proofgold Signed Transaction

Param lam_id^lam_id : ι → ι
Param ap^ap : ι → ι → ι
Definition struct_id^struct_id := λ x0 . lam_id (ap x0 0)
Param lam_comp^lam_comp : ι → ι → ι → ι
Definition struct_comp^struct_comp := λ x0 x1 x2 . lam_comp (ap x0 0)
Param and^and : ο → ο → ο
Param PreContinuousHom^Hom_struct_c : ι → ι → ι → ο
Param UnaryFuncHom^Hom_struct_u : ι → ι → ι → ο
Param UnaryPredHom^Hom_struct_p : ι → ι → ι → ο
Definition 48280.. := λ x0 x1 x2 . and (and (PreContinuousHom x0 x1 x2) (UnaryFuncHom x0 x1 x2)) (UnaryPredHom x0 x1 x2)
Param MetaCat_initial_p^initial_p : (ι → ο) → (ι → ι → ι → ο) → (ι → ι) → (ι → ι → ι → ι → ι → ι) → ι → (ι → ι) → ο
Param struct_c_u_p : ι → ο
Conjecture 47b6b.. : ∀ x0 : ο . (∀ x1 . (∀ x2 : ο . (∀ x3 : ι → ι . MetaCat_initial_p struct_c_u_p 48280.. struct_id struct_comp x1 x3 ⟶ x2) ⟶ x2) ⟶ x0) ⟶ x0
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 10225.. : ∀ x0 : ο . (∀ x1 . (∀ x2 : ο . (∀ x3 : ι → ι . MetaCat_terminal_p struct_c_u_p 48280.. 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 f6a5c.. : ∀ 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_c_u_p 48280.. 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 cae90.. : ∀ 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_c_u_p 48280.. 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 5886f.. : ∀ 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_c_u_p 48280.. 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 6d4ed.. : ∀ 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_c_u_p 48280.. 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 8348d.. : ∀ 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_c_u_p 48280.. 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 17320.. : ∀ 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_c_u_p 48280.. 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 74e3d.. : ∀ 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_c_u_p 48280.. 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 08a6f.. : ∀ 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_c_u_p 48280.. 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 1b5af.. : ∀ 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_c_u_p 48280.. 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
Param HomSet^SetHom : ι → ι → ι → ο
Conjecture 3bbae.. : ∀ 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_c_u_p 48280.. 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