Apply unknownprop_f23dde3020cfe827bdc4db0338b279dd2c0f6c90742a195a1a7a614475669076 with
λ x0 . mul_nat 0 x0 = 0 leaving 2 subgoals.
The subproof is completed by applying unknownprop_4756ca8c34efd0461ee4f316febaf4ee77ac8f03a3f9f75c481b60c5f8500b17 with 0.
Let x0 of type ι be given.
Apply unknownprop_3defe724d02ba276d9730f9f5a87e86e6bc0e48da350a99bdaaf13f339867dcf with
0,
x0,
λ x1 x2 . x2 = 0 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply H1 with
λ x1 x2 . add_nat 0 x2 = 0.
The subproof is completed by applying unknownprop_bad5adbbba30ab6e9c584ed350d824b3c3bff74e61c0a5380ac75f32855c37ee with 0.