Let x0 of type ι be given.
Let x1 of type ι be given.
Apply H0 with
λ x2 x3 . prim1 x0 x2.
The subproof is completed by applying unknownprop_38ce50d6b52a0a920b530e7796207ec902a42d65414467df1ecd3efb123f4cb9 with x0.
Apply unknownprop_dec2978c0a72cebd51fcab0a380f03d4d80d1ccd8f826d378953148c305a60f0 with
x1,
x0,
x0 = x1 leaving 3 subgoals.
The subproof is completed by applying L1.
Apply H0 with
λ x2 x3 . prim1 x1 x3.
The subproof is completed by applying unknownprop_38ce50d6b52a0a920b530e7796207ec902a42d65414467df1ecd3efb123f4cb9 with x1.
Apply unknownprop_dec2978c0a72cebd51fcab0a380f03d4d80d1ccd8f826d378953148c305a60f0 with
x0,
x1,
x0 = x1 leaving 3 subgoals.
The subproof is completed by applying L3.
Apply FalseE with
x0 = x1.
Apply unknownprop_f1a526a64fd91875cd825eea7f2e7776b7f0e7be5dcee74dc03af1d7886d1eb6 with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H4.
Assume H4: x1 = x0.
Let x2 of type ι → ι → ο be given.
The subproof is completed by applying H4 with λ x3 x4 . x2 x4 x3.
Assume H2: x0 = x1.
The subproof is completed by applying H2.