Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_c3fe42b21df0810041479a97b374de73f7754e07c8af1c88386a1e7dc0aad10f with
x1,
x0.
Let x2 of type ι be given.
Apply unknownprop_84fe37a922385756a4e0826a593defb788cadbe4bdc9a7fe6b519ea49f509df5 with
x0,
x1,
In x2 x0 leaving 3 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_cc8f63ddfbec05087d89028647ba2c7b89da93a15671b61ba228d6841bbab5e9 with
x1,
x0,
x2 leaving 2 subgoals.
Apply unknownprop_92b4103b83752522eb6c235601eefa2912e3f6395a346e3a7eb52bb5e37ede81 with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.
The subproof is completed by applying H2.
Assume H3: x1 = x0.
Apply H3 with
λ x3 x4 . In x2 x3.
The subproof is completed by applying H2.