Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_f23dde3020cfe827bdc4db0338b279dd2c0f6c90742a195a1a7a614475669076 with
λ x2 . add_nat x0 x2 = add_nat x1 x2 ⟶ x0 = x1 leaving 2 subgoals.
Apply unknownprop_bad5adbbba30ab6e9c584ed350d824b3c3bff74e61c0a5380ac75f32855c37ee with
x0,
λ x2 x3 . x3 = add_nat x1 0 ⟶ x0 = x1.
Apply unknownprop_bad5adbbba30ab6e9c584ed350d824b3c3bff74e61c0a5380ac75f32855c37ee with
x1,
λ x2 x3 . x0 = x3 ⟶ x0 = x1.
Assume H0: x0 = x1.
The subproof is completed by applying H0.
Let x2 of type ι be given.
Apply unknownprop_bfc870f6d786cc78805c5bf0f9864161d18f532f6daf7daf1d02f4a58dac06f9 with
x0,
x2,
λ x3 x4 . x4 = add_nat x1 (ordsucc x2) ⟶ x0 = x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_bfc870f6d786cc78805c5bf0f9864161d18f532f6daf7daf1d02f4a58dac06f9 with
x1,
x2,
λ x3 x4 . ordsucc (add_nat x0 x2) = x4 ⟶ x0 = x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply H1.
Apply unknownprop_60abe2ef0ccd78a594794787666c926523153e194cc1f57a533bf14f6930c3c8 with
add_nat x0 x2,
add_nat x1 x2.
The subproof is completed by applying H2.