Let x0 of type ι → ο be given.
Assume H0:
(λ x1 : ι → ο . ∀ x2 : (ι → ο) → ο . (∀ x3 : ι → ο . x2 x3 ⟶ x2 ((λ x4 : ι → ο . λ x5 . and (x4 x5) (x5 = prim0 (λ x6 . x4 x6) ⟶ ∀ x6 : ο . x6)) x3)) ⟶ (∀ x3 : (ι → ο) → ο . (∀ x4 : ι → ο . x3 x4 ⟶ x2 x4) ⟶ x2 (Descr_Vo1 x3)) ⟶ x2 x1) x0.
Apply H0 with
λ x1 : ι → ο . ∀ x2 : ι → ο . (λ x3 : ι → ο . ∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . x4 x5 ⟶ x4 ((λ x6 : ι → ο . λ x7 . and (x6 x7) (x7 = prim0 (λ x8 . x6 x8) ⟶ ∀ x8 : ο . x8)) x5)) ⟶ (∀ x5 : (ι → ο) → ο . (∀ x6 : ι → ο . x5 x6 ⟶ x4 x6) ⟶ x4 (Descr_Vo1 x5)) ⟶ x4 x3) x2 ⟶ or (∀ x3 . x2 x3 ⟶ x1 x3) (∀ x3 . x1 x3 ⟶ x2 x3) leaving 2 subgoals.
Let x1 of type ι → ο be given.
Assume H1:
∀ x2 : ι → ο . (λ x3 : ι → ο . ∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . x4 x5 ⟶ x4 ((λ x6 : ι → ο . λ x7 . and (x6 x7) (x7 = prim0 (λ x8 . x6 x8) ⟶ ∀ x8 : ο . x8)) x5)) ⟶ (∀ x5 : (ι → ο) → ο . (∀ x6 : ι → ο . x5 x6 ⟶ x4 x6) ⟶ x4 (Descr_Vo1 x5)) ⟶ x4 x3) x2 ⟶ or (∀ x3 . x2 x3 ⟶ x1 x3) (∀ x3 . x1 x3 ⟶ x2 x3).
Apply unknownprop_8b6c35c0be5cf8f722ca2f225499fd1f64fbc0efe96a58d22f31aad0a1ec0140 with
λ x2 : ι → ο . or (∀ x3 . x2 x3 ⟶ (λ x4 : ι → ο . λ x5 . and (x4 x5) (x5 = prim0 (λ x6 . x4 x6) ⟶ ∀ x6 : ο . x6)) x1 x3) (∀ x3 . (λ x4 : ι → ο . λ x5 . and (x4 x5) (x5 = prim0 (λ x6 . x4 x6) ⟶ ∀ x6 : ο . x6)) x1 x3 ⟶ x2 x3) leaving 2 subgoals.
Let x2 of type ι → ο be given.
Assume H2:
(λ x3 : ι → ο . ∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . x4 x5 ⟶ x4 ((λ x6 : ι → ο . λ x7 . and (x6 x7) (x7 = prim0 (λ x8 . x6 x8) ⟶ ∀ x8 : ο . x8)) x5)) ⟶ (∀ x5 : (ι → ο) → ο . (∀ x6 : ι → ο . x5 x6 ⟶ x4 x6) ⟶ x4 (Descr_Vo1 x5)) ⟶ x4 x3) x2.
Assume H3:
or (∀ x3 . x2 x3 ⟶ (λ x4 : ι → ο . λ x5 . and (x4 x5) (x5 = prim0 (λ x6 . x4 x6) ⟶ ∀ x6 : ο . x6)) x1 x3) (∀ x3 . (λ x4 : ι → ο . λ x5 . and (x4 x5) (x5 = prim0 (λ x6 . x4 x6) ⟶ ∀ x6 : ο . x6)) x1 x3 ⟶ x2 x3).
Apply H3 with
or (∀ x3 . (λ x4 : ι → ο . λ x5 . and (x4 x5) (... ⟶ ∀ x6 : ο . x6)) ... ... ⟶ (λ x4 : ι → ο . λ x5 . and (x4 x5) (x5 = prim0 (λ x6 . x4 x6) ⟶ ∀ x6 : ο . x6)) x1 x3) ... leaving 2 subgoals.