Let x0 of type ι be given.
Let x1 of type ι → ο be given.
Assume H1:
∀ x2 . In x2 x0 ⟶ ∀ x3 . In x3 x2 ⟶ x1 x2 ⟶ x1 x3.
Apply unknownprop_5273a64cd2d40c560fbf5871c7601206337acc93fe8f7292cc8c65a171682421 with
λ x2 x3 : ι → ο . x3 (Sep x0 (λ x4 . x1 x4)).
Apply unknownprop_389e2fb1855352fcc964ea44fe6723d7a1c2d512f04685300e3e97621725b977 with
TransSet (Sep x0 (λ x2 . x1 x2)),
∀ x2 . In x2 (Sep x0 (λ x3 . x1 x3)) ⟶ TransSet x2 leaving 2 subgoals.
Apply unknownprop_867ee8b2da9f256b3418dab3ba4978d6cabdc87fec1095d8f8aa46324a9136f8 with
Sep x0 (λ x2 . x1 x2).
Let x2 of type ι be given.
Assume H2:
In x2 (Sep x0 (λ x3 . x1 x3)).
Apply unknownprop_c3fe42b21df0810041479a97b374de73f7754e07c8af1c88386a1e7dc0aad10f with
x2,
Sep x0 (λ x3 . x1 x3).
Let x3 of type ι be given.
Apply unknownprop_6a6b356f855b99f3fbff4effcb62e3ee6aa23839e10650eb28a503a368c2bb09 with
x0,
x1,
x2,
In x3 (Sep x0 (λ x4 . x1 x4)) leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H5: x1 x2.
Apply unknownprop_646b3add51cf8f8e84959b456822a93c7e59b2f394a14897b6752b9d28c1a75d with
x0,
x1,
x3 leaving 2 subgoals.
Apply unknownprop_cc8f63ddfbec05087d89028647ba2c7b89da93a15671b61ba228d6841bbab5e9 with
x2,
x0,
x3 leaving 2 subgoals.
Apply unknownprop_5af24edc592c6d7fa3cf53e40211635bbed8f39380469ac8aef3490ee700739c with
x0,
x2 leaving 2 subgoals.
Apply unknownprop_e682831a7124f89af4a1b1d248afbcd452dfbbb9d90b9a88db6885fe36808b65 with
x0.
The subproof is completed by applying H0.
The subproof is completed by applying H4.
The subproof is completed by applying H3.
Apply H1 with
x2,
x3 leaving 3 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H3.
The subproof is completed by applying H5.
Let x2 of type ι be given.
Assume H2:
In x2 (Sep x0 (λ x3 . x1 x3)).
Apply unknownprop_dde4f02836f1e21077854af0376b49f8617a754506141458ada04e8c79a76b89 with
x0,
x1,
x2.
The subproof is completed by applying H2.
Apply unknownprop_df95567eaac7dcf742571a06351d685ef037c3575a0b273f643efe646824ac1a with
x0,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L3.
Apply unknownprop_e682831a7124f89af4a1b1d248afbcd452dfbbb9d90b9a88db6885fe36808b65 with
x2.
The subproof is completed by applying L4.