Apply unknownprop_f23dde3020cfe827bdc4db0338b279dd2c0f6c90742a195a1a7a614475669076 with
λ x0 . add_nat 0 x0 = x0 leaving 2 subgoals.
The subproof is completed by applying unknownprop_bad5adbbba30ab6e9c584ed350d824b3c3bff74e61c0a5380ac75f32855c37ee with 0.
Let x0 of type ι be given.
Apply unknownprop_bfc870f6d786cc78805c5bf0f9864161d18f532f6daf7daf1d02f4a58dac06f9 with
0,
x0,
λ x1 x2 . x2 = ordsucc x0 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply H1 with
λ x1 x2 . ordsucc x2 = ordsucc x0.
Let x1 of type ι → ι → ο be given.
The subproof is completed by applying H2.