Let x0 of type ι be given.
Apply H0 with
∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι → ο . x2 = 0 ⟶ x1 (pack_r x2 x3)) ⟶ x1 x0.
Apply H1 with
λ x1 . unpack_r_o x1 (λ x2 . λ x3 : ι → ι → ο . and (and (∀ x4 . x4 ∈ x2 ⟶ not (x3 x4 x4)) (∀ x4 . x4 ∈ x2 ⟶ ∀ x5 . x5 ∈ x2 ⟶ or (x3 x4 x5) (x3 x5 x4))) (∀ x4 . x4 ∈ x2 ⟶ ∀ x5 . x5 ∈ x2 ⟶ ∀ x6 . x6 ∈ x2 ⟶ x3 x4 x5 ⟶ x3 x5 x6 ⟶ x3 x4 x6)) ⟶ ∀ x2 : ι → ο . (∀ x3 . ∀ x4 : ι → ι → ο . x3 = 0 ⟶ x2 (pack_r x3 x4)) ⟶ x2 x1.
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Apply unknownprop_a4bb8825cdd8d49d4389d22179d1719a0b873e5d71045f76904774492ae46207 with
x1,
x2,
λ x3 x4 : ο . x4 ⟶ ∀ x5 : ι → ο . (∀ x6 . ∀ x7 : ι → ι → ο . x6 = 0 ⟶ x5 (pack_r x6 x7)) ⟶ x5 (pack_r x1 x2).
Assume H2:
and (and (∀ x3 . x3 ∈ x1 ⟶ not (x2 x3 x3)) (∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ or (x2 x3 x4) (x2 x4 x3))) (∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ ∀ x5 . x5 ∈ x1 ⟶ x2 x3 x4 ⟶ x2 x4 x5 ⟶ x2 x3 x5).
Apply H2 with
∀ x3 : ι → ο . (∀ x4 . ∀ x5 : ι → ι → ο . x4 = 0 ⟶ x3 (pack_r x4 x5)) ⟶ x3 (pack_r x1 x2).
Assume H3:
and (∀ x3 . x3 ∈ x1 ⟶ not (x2 x3 x3)) (∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ or (x2 x3 x4) (x2 x4 x3)).
Apply H3 with
(∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ ∀ x5 . x5 ∈ x1 ⟶ x2 x3 x4 ⟶ x2 x4 x5 ⟶ x2 x3 x5) ⟶ ∀ x3 : ι → ο . (∀ x4 . ∀ x5 : ι → ι → ο . x4 = 0 ⟶ x3 (pack_r x4 x5)) ⟶ x3 (pack_r x1 x2).
Assume H4:
∀ x3 . x3 ∈ x1 ⟶ not (x2 x3 x3).
Assume H5:
∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ or (x2 x3 x4) (x2 x4 x3).
Assume H6: ∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ ∀ x5 . x5 ∈ x1 ⟶ x2 x3 x4 ⟶ x2 x4 x5 ⟶ x2 x3 x5.
Let x3 of type ι → ο be given.