Let x0 of type ι be given.
Apply unknownprop_f23dde3020cfe827bdc4db0338b279dd2c0f6c90742a195a1a7a614475669076 with
λ x1 . nat_p (add_nat x0 x1) leaving 2 subgoals.
Apply unknownprop_bad5adbbba30ab6e9c584ed350d824b3c3bff74e61c0a5380ac75f32855c37ee with
x0,
λ x1 x2 . nat_p x2.
The subproof is completed by applying H0.
Let x1 of type ι be given.
Apply unknownprop_bfc870f6d786cc78805c5bf0f9864161d18f532f6daf7daf1d02f4a58dac06f9 with
x0,
x1,
λ x2 x3 . nat_p x3 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_077979b790f9097ea9250573e60509ec9410103c35a67e0558983ee18582fb09 with
add_nat x0 x1.
The subproof is completed by applying H2.