Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_f23dde3020cfe827bdc4db0338b279dd2c0f6c90742a195a1a7a614475669076 with
λ x2 . add_nat (add_nat x0 x1) x2 = add_nat x0 (add_nat x1 x2) leaving 2 subgoals.
Apply unknownprop_bad5adbbba30ab6e9c584ed350d824b3c3bff74e61c0a5380ac75f32855c37ee with
add_nat x0 x1,
λ x2 x3 . x3 = add_nat x0 (add_nat x1 0).
Apply unknownprop_bad5adbbba30ab6e9c584ed350d824b3c3bff74e61c0a5380ac75f32855c37ee with
x1,
λ x2 x3 . add_nat x0 x1 = add_nat x0 x3.
Let x2 of type ι → ι → ο be given.
The subproof is completed by applying H1.
Let x2 of type ι be given.
Apply unknownprop_bfc870f6d786cc78805c5bf0f9864161d18f532f6daf7daf1d02f4a58dac06f9 with
add_nat x0 x1,
x2,
λ x3 x4 . x4 = add_nat x0 (add_nat x1 (ordsucc x2)) leaving 2 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_bfc870f6d786cc78805c5bf0f9864161d18f532f6daf7daf1d02f4a58dac06f9 with
x1,
x2,
λ x3 x4 . ordsucc (add_nat (add_nat x0 x1) x2) = add_nat x0 x4 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_bfc870f6d786cc78805c5bf0f9864161d18f532f6daf7daf1d02f4a58dac06f9 with
x0,
add_nat x1 x2,
λ x3 x4 . ordsucc (add_nat (add_nat x0 x1) x2) = x4 leaving 2 subgoals.
Apply unknownprop_3336121954edce0fefb5edee2ad1b426a9827aac09625122db0ff807b493dc73 with
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply H2 with
λ x3 x4 . ordsucc x4 = ordsucc (add_nat x0 (add_nat x1 x2)).
Let x3 of type ι → ι → ο be given.
The subproof is completed by applying H3.