Let x0 of type ι be given.
Apply unknownprop_f23dde3020cfe827bdc4db0338b279dd2c0f6c90742a195a1a7a614475669076 with
λ x1 . add_nat x0 x1 = add_nat x1 x0 leaving 2 subgoals.
Apply unknownprop_df54193808dbf362a1639247261ed5d96fbe79793df63d3adf7cbfabe00d07b2 with
x0,
λ x1 x2 . add_nat x0 0 = x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying unknownprop_bad5adbbba30ab6e9c584ed350d824b3c3bff74e61c0a5380ac75f32855c37ee with x0.
Let x1 of type ι be given.
Apply unknownprop_d3d30a4c72d970b9282cfa73c76d5a7e8c72c3511a5fbd572a3d9a9086e00acb with
x1,
x0,
λ x2 x3 . add_nat x0 (ordsucc x1) = x3 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Apply H2 with
λ x2 x3 . add_nat x0 (ordsucc x1) = ordsucc x2.
Apply unknownprop_bfc870f6d786cc78805c5bf0f9864161d18f532f6daf7daf1d02f4a58dac06f9 with
x0,
x1.
The subproof is completed by applying H1.