Let x0 of type ι be given.
Apply unknownprop_f23dde3020cfe827bdc4db0338b279dd2c0f6c90742a195a1a7a614475669076 with
λ x1 . Subq x0 (add_nat x0 x1) leaving 2 subgoals.
Apply unknownprop_bad5adbbba30ab6e9c584ed350d824b3c3bff74e61c0a5380ac75f32855c37ee with
x0,
λ x1 x2 . Subq x0 x2.
The subproof is completed by applying unknownprop_d889823a5c975ad2d68f484964233a1e69e7d67f0888aa5b83d962eeca107acd with x0.
Let x1 of type ι be given.
Apply unknownprop_bfc870f6d786cc78805c5bf0f9864161d18f532f6daf7daf1d02f4a58dac06f9 with
x0,
x1,
λ x2 x3 . Subq x0 x3 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_16d2e0ac4e61f9d6f4710f68fd29bc0751fdb2a43ae4ee41dc39565d6502f8a7 with
x0,
add_nat x0 x1,
ordsucc (add_nat x0 x1) leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying unknownprop_b2bebb8105f29e822888ab2d4b10db11282fc91a7326e3993f508ffc07b3af08 with
add_nat x0 x1.