Let x0 of type ι be given.
Apply H0 with
∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι → ο . (∀ x4 . x4 ∈ x2 ⟶ not (x3 x4 x4)) ⟶ (∀ x4 . x4 ∈ x2 ⟶ ∀ x5 . x5 ∈ x2 ⟶ x3 x4 x5 ⟶ x3 x5 x4) ⟶ x1 (pack_r x2 x3)) ⟶ x1 x0.
Apply H1 with
λ x1 . unpack_r_o x1 (λ x2 . λ x3 : ι → ι → ο . and (∀ x4 . x4 ∈ x2 ⟶ not (x3 x4 x4)) (∀ x4 . x4 ∈ x2 ⟶ ∀ x5 . x5 ∈ x2 ⟶ x3 x4 x5 ⟶ x3 x5 x4)) ⟶ ∀ x2 : ι → ο . (∀ x3 . ∀ x4 : ι → ι → ο . (∀ x5 . x5 ∈ x3 ⟶ not (x4 x5 x5)) ⟶ (∀ x5 . x5 ∈ x3 ⟶ ∀ x6 . x6 ∈ x3 ⟶ x4 x5 x6 ⟶ x4 x6 x5) ⟶ 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_ee6d5f0119c23d2d365410bede08f376d1ae2b56e8e57cf05f64e993f9b9e31e with
x1,
x2,
λ x3 x4 : ο . x4 ⟶ ∀ x5 : ι → ο . (∀ x6 . ∀ x7 : ι → ι → ο . (∀ x8 . x8 ∈ x6 ⟶ not (x7 x8 x8)) ⟶ (∀ x8 . x8 ∈ x6 ⟶ ∀ x9 . x9 ∈ x6 ⟶ x7 x8 x9 ⟶ x7 x9 x8) ⟶ x5 (pack_r x6 x7)) ⟶ x5 (pack_r x1 x2).
Assume H2:
and (∀ x3 . x3 ∈ x1 ⟶ not (x2 x3 x3)) (∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ x2 x3 x4 ⟶ x2 x4 x3).
Apply H2 with
∀ x3 : ι → ο . (∀ x4 . ∀ x5 : ι → ι → ο . (∀ x6 . x6 ∈ x4 ⟶ not (x5 x6 x6)) ⟶ (∀ x6 . x6 ∈ x4 ⟶ ∀ x7 . x7 ∈ x4 ⟶ x5 x6 x7 ⟶ x5 x7 x6) ⟶ x3 (pack_r x4 x5)) ⟶ x3 (pack_r x1 x2).
Assume H3:
∀ x3 . x3 ∈ x1 ⟶ not (x2 x3 x3).
Assume H4: ∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ x2 x3 x4 ⟶ x2 x4 x3.
Let x3 of type ι → ο be given.
Assume H5:
∀ x4 . ∀ x5 : ι → ι → ο . (∀ x6 . x6 ∈ x4 ⟶ not (x5 x6 x6)) ⟶ (∀ x6 . x6 ∈ x4 ⟶ ∀ x7 . x7 ∈ x4 ⟶ x5 x6 x7 ⟶ x5 x7 x6) ⟶ x3 (pack_r x4 x5).
Apply H5 with
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.