Let x0 of type ο be given.
Apply H0 with
pack_r 0 (λ x1 x2 . False).
Let x1 of type ο be given.
Apply H1 with
λ x2 . 0.
Apply andI with
90aea.. (pack_r 0 (λ x2 x3 . False)),
∀ x2 . 90aea.. x2 ⟶ and (BinRelnHom (pack_r 0 (λ x3 x4 . False)) x2 0) (∀ x3 . BinRelnHom (pack_r 0 (λ x4 x5 . False)) x2 x3 ⟶ x3 = 0) leaving 2 subgoals.
The subproof is completed by applying unknownprop_368e92f67c0383aee9043344ceeddddb8cd4a69474da241bb811d114c3a8b2be.
Let x2 of type ι be given.
Apply unknownprop_589446c7eb1e0f49f9a1c9ecf95332e51a36bcf398bd883c8295d2920f123b6b with
pack_r 0 (λ x3 x4 . False),
x2,
0,
λ x3 x4 : ο . and x4 (∀ x5 . BinRelnHom (pack_r 0 (λ x6 x7 . False)) x2 x5 ⟶ x5 = 0) leaving 3 subgoals.
The subproof is completed by applying unknownprop_368e92f67c0383aee9043344ceeddddb8cd4a69474da241bb811d114c3a8b2be.
The subproof is completed by applying H2.
Apply andI with
0 = 0,
∀ x3 . BinRelnHom (pack_r 0 (λ x4 x5 . False)) x2 x3 ⟶ x3 = 0 leaving 2 subgoals.
Let x3 of type ι → ι → ο be given.
Assume H3: x3 0 0.
The subproof is completed by applying H3.
Let x3 of type ι be given.
Apply unknownprop_589446c7eb1e0f49f9a1c9ecf95332e51a36bcf398bd883c8295d2920f123b6b with
pack_r 0 (λ x4 x5 . False),
x2,
x3,
λ x4 x5 : ο . x5 ⟶ x3 = 0 leaving 3 subgoals.
The subproof is completed by applying unknownprop_368e92f67c0383aee9043344ceeddddb8cd4a69474da241bb811d114c3a8b2be.
The subproof is completed by applying H2.
Assume H3: x3 = 0.
The subproof is completed by applying H3.