Let x0 of type ι be given.
Apply unknownprop_f23dde3020cfe827bdc4db0338b279dd2c0f6c90742a195a1a7a614475669076 with
λ x1 . add_nat (ordsucc x0) x1 = ordsucc (add_nat x0 x1) leaving 2 subgoals.
Apply unknownprop_bad5adbbba30ab6e9c584ed350d824b3c3bff74e61c0a5380ac75f32855c37ee with
ordsucc x0,
λ x1 x2 . x2 = ordsucc (add_nat x0 0).
Apply unknownprop_bad5adbbba30ab6e9c584ed350d824b3c3bff74e61c0a5380ac75f32855c37ee with
x0,
λ x1 x2 . ordsucc x0 = ordsucc x2.
Let x1 of type ι → ι → ο be given.
The subproof is completed by applying H1.
Let x1 of type ι be given.
Apply unknownprop_bfc870f6d786cc78805c5bf0f9864161d18f532f6daf7daf1d02f4a58dac06f9 with
ordsucc x0,
x1,
λ x2 x3 . x3 = ordsucc (add_nat x0 (ordsucc x1)) leaving 2 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_bfc870f6d786cc78805c5bf0f9864161d18f532f6daf7daf1d02f4a58dac06f9 with
x0,
x1,
λ x2 x3 . ordsucc (add_nat (ordsucc x0) x1) = ordsucc x3 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply H2 with
λ x2 x3 . ordsucc x3 = ordsucc (ordsucc (add_nat x0 x1)).
Let x2 of type ι → ι → ο be given.
The subproof is completed by applying H3.