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Proofgold Proof

pf
Let x0 of type ο be given.
Assume H0: ∀ x1 : ι → ι . (∃ x2 : ι → ι → ι → ι . ∃ x3 x4 : ι → ι . MetaAdjunction_strict (λ x5 . True) HomSet (λ x5 . lam_id x5) (λ x5 x6 x7 x8 x9 . lam_comp x5 x8 x9) struct_p UnaryPredHom struct_id struct_comp x1 x2 (λ x5 . ap x5 0) (λ x5 x6 x7 . x7) x3 x4) ⟶ x0.
Apply H0 with λ x1 . pack_p x1 (λ x2 . False).
Let x1 of type ο be given.
Assume H1: ∀ x2 : ι → ι → ι → ι . (∃ x3 x4 : ι → ι . MetaAdjunction_strict (λ x5 . True) HomSet (λ x5 . lam_id x5) (λ x5 x6 x7 x8 x9 . lam_comp x5 x8 x9) struct_p UnaryPredHom struct_id struct_comp (λ x5 . pack_p x5 (λ x6 . False)) x2 (λ x5 . ap x5 0) (λ x5 x6 x7 . x7) x3 x4) ⟶ x1.
Apply H1 with λ x2 x3 x4 . x4.
Let x2 of type ο be given.
Assume H2: ∀ x3 : ι → ι . (∃ x4 : ι → ι . MetaAdjunction_strict (λ x5 . True) HomSet (λ x5 . lam_id x5) (λ x5 x6 x7 x8 x9 . lam_comp x5 x8 x9) struct_p UnaryPredHom struct_id struct_comp (λ x5 . pack_p x5 (λ x6 . False)) (λ x5 x6 x7 . x7) (λ x5 . ap x5 0) (λ x5 x6 x7 . x7) x3 x4) ⟶ x2.
Apply H2 with λ x3 . lam_id x3.
Let x3 of type ο be given.
Assume H3: ∀ x4 : ι → ι . MetaAdjunction_strict (λ x5 . True) HomSet (λ x5 . lam_id x5) (λ x5 x6 x7 x8 x9 . lam_comp x5 x8 x9) struct_p UnaryPredHom struct_id struct_comp (λ x5 . pack_p x5 (λ x6 . False)) (λ x5 x6 x7 . x7) (λ x5 . ap x5 0) (λ x5 x6 x7 . x7) (λ x5 . lam_id x5) x4 ⟶ x3.
Apply H3 with λ x4 . lam_id (ap x4 0).
Claim L4: ...
...
Claim L5: ...
...
Claim L6: ...
...
Claim L7: ...
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Apply unknownprop_712520f713b96d5afd10321cea9a3c978868fc53aa35a29461e902d5b5a4ba79 with λ x4 . True, HomSet, λ x4 . lam_id x4, λ x4 x5 x6 x7 x8 . lam_comp x4 x7 x8, struct_p, UnaryPredHom, struct_id, struct_comp, λ x4 . pack_p x4 (λ x5 . False), λ x4 x5 x6 . x6, λ x4 . ap x4 0, λ x4 x5 x6 . x6, λ x4 . lam_id x4, λ x4 . lam_id (ap x4 0) leaving 5 subgoals.
Apply unknownprop_3d05796578cdc17ebd2096167db48ecef934256d250d1637eb5dd67225cdfe05 with λ x4 . True, HomSet, λ x4 . lam_id x4, λ x4 x5 x6 x7 x8 . lam_comp x4 x7 x8, struct_p, UnaryPredHom, struct_id, struct_comp, λ x4 . pack_p x4 (λ x5 . False), λ x4 x5 x6 . x6 leaving 3 subgoals.
The subproof is completed by applying unknownprop_dcf5739aa5fe0adc626fd983737b233fe68652dff14c53b3d75823dcf2542d41.
The subproof is completed by applying unknownprop_edb0bbc1cf315b54e2af6e88f0ad67b20f207887129fd2bc159319d8845a3b71.
Apply unknownprop_795e291855a044d4d636c961caa1600704603cc02e33a7b37aa66e8d7f6512db with λ x4 . True, HomSet, λ x4 . lam_id x4, λ x4 x5 x6 x7 x8 . lam_comp x4 x7 x8, struct_p, UnaryPredHom, struct_id, struct_comp, λ x4 . pack_p x4 (λ x5 . False), λ x4 x5 x6 . x6 leaving 4 subgoals.
Let x4 of type ι be given.
Assume H8: (λ x5 . True) x4.
The subproof is completed by applying L4 with x4.
Let x4 of type ι be given.
Let x5 of type ι be given.
Let x6 of type ι be given.
Assume H8: (λ x7 . True) x4.
Assume H9: (λ x7 . True) x5.
Assume H10: HomSet x4 x5 x6.
Apply L6 with x4, x5, x6.
The subproof is completed by applying H10.
Let x4 of type ι be given.
Assume H8: (λ x5 . True) x4.
set y5 to be ...
set y6 to be ...
Claim L9: ...
...
Let x7 of type ι → ι → ο be given.
Apply L9 with λ x8 . x7 ... ... ⟶ x7 y6 x8.
...
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...
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