Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_c3fe42b21df0810041479a97b374de73f7754e07c8af1c88386a1e7dc0aad10f with
x0,
x1.
Let x2 of type ι be given.
Apply H1 with
λ x3 x4 . In x2 x3.
Apply unknownprop_c8252e4c83bb4898d143266bc455e2432960bbe927d91a6293e89e924042d02d with
x0,
Sing 1,
x2.
The subproof is completed by applying H2.
Apply unknownprop_e0504d591aa31271c5372c445c216da1b623d835d8188df9ffa1d2ea977ac098 with
x1,
Sing 1,
x2,
In x2 x1 leaving 3 subgoals.
The subproof is completed by applying L3.
The subproof is completed by applying H4.
Apply FalseE with
In x2 x1.
Apply unknownprop_831031d8fe8dbf34401419f1bd72d9257a766bdbb899a9b13b9b87ffc267e396.
Apply H4 with
λ x3 x4 . ordinal x3.
Apply unknownprop_df95567eaac7dcf742571a06351d685ef037c3575a0b273f643efe646824ac1a with
x0,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.