Apply unknownprop_acac0f89c78f08b97a9fe27ba4af5f929f74e43a9a77a0beb38d70975279c8b8 with
λ x0 . ∀ x1 . Subq x0 (V_ x1) ⟶ Subq (V_ x0) (V_ x1).
Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_c3fe42b21df0810041479a97b374de73f7754e07c8af1c88386a1e7dc0aad10f with
V_ x0,
V_ x1.
Let x2 of type ι be given.
Assume H2:
In x2 (V_ x0).
Apply unknownprop_3687558d9284fdd514174bfe87bba39032212334a6409eb4554d4077dea6d831 with
x2,
x0,
In x2 (V_ x1) leaving 2 subgoals.
The subproof is completed by applying H2.
Let x3 of type ι be given.
Apply unknownprop_cc8f63ddfbec05087d89028647ba2c7b89da93a15671b61ba228d6841bbab5e9 with
x0,
V_ x1,
x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Apply unknownprop_3687558d9284fdd514174bfe87bba39032212334a6409eb4554d4077dea6d831 with
x3,
x1,
In x2 (V_ x1) leaving 2 subgoals.
The subproof is completed by applying L5.
Let x4 of type ι be given.
Apply H0 with
x3,
x4 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H7.
Apply unknownprop_16d2e0ac4e61f9d6f4710f68fd29bc0751fdb2a43ae4ee41dc39565d6502f8a7 with
x2,
V_ x3,
V_ x4 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying L8.
Apply unknownprop_a2c3fca2e8c461af2fcd2014916bc97ec486da998a233beedf90ec14d6bf2e76 with
x2,
x4,
x1 leaving 2 subgoals.
The subproof is completed by applying H6.
The subproof is completed by applying L9.