Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_1f03c3e4cc230143731a84d6351b78522f6051d5113f644774435abf9cb5a984 with
x1.
Apply ordinal_Hered with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply ordinal_trichotomy_or with
x0,
4ae4a.. x1,
or (prim1 (4ae4a.. x1) x0) (x0 = 4ae4a.. x1) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L2.
Apply H3 with
or (prim1 (4ae4a.. x1) x0) (x0 = 4ae4a.. x1) leaving 2 subgoals.
Apply FalseE with
or (prim1 (4ae4a.. x1) x0) (x0 = 4ae4a.. x1).
Apply unknownprop_dec2978c0a72cebd51fcab0a380f03d4d80d1ccd8f826d378953148c305a60f0 with
x1,
x0,
False leaving 3 subgoals.
The subproof is completed by applying H4.
Apply unknownprop_f1a526a64fd91875cd825eea7f2e7776b7f0e7be5dcee74dc03af1d7886d1eb6 with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H5.
The subproof is completed by applying H1.
Assume H5: x0 = x1.
Apply In_irref with
x0.
Apply H5 with
λ x2 x3 . prim1 x3 x0.
The subproof is completed by applying H1.
Apply orIR with
prim1 (4ae4a.. x1) x0,
x0 = 4ae4a.. x1.
The subproof is completed by applying H4.
Apply orIL with
prim1 (4ae4a.. x1) x0,
x0 = 4ae4a.. x1.
The subproof is completed by applying H3.