Let x0 of type ι → (ι → ο) → ο be given.
Let x1 of type ι → (ι → ο) → ο be given.
Let x2 of type ι be given.
Let x3 of type ι → ο be given.
Apply andI with
8033b.. x0 x1 (4ae4a.. x2) (λ x4 . and (x3 x4) (x4 = x2 ⟶ ∀ x5 : ο . x5)),
8033b.. x0 x1 (4ae4a.. x2) (λ x4 . or (x3 x4) (x4 = x2)) leaving 2 subgoals.
Apply unknownprop_e4e26e97d7c9268ddd58ec854c827faf28de9e025ff66b7534f09954deeb2bfd with
x0,
x1,
x2,
x3 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply unknownprop_9906d38914209c1864dcba49ac13f0a83dd2a7e77e2e8964644942aa1246e77e with
x0,
x1,
x2,
x3 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.