Let x0 of type ι → ο be given.
Let x1 of type ι be given.
Assume H0: x0 x1.
Let x2 of type ι → ο be given.
Assume H1:
and ((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) (∀ x3 . x0 x3 ⟶ x2 x3).
Apply andER with
(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,
∀ x3 . x0 x3 ⟶ x2 x3,
x1 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.