Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H2: x2 ∈ x1.
Apply add_nat_com with
x0,
x2,
λ x3 x4 . x4 ∈ add_nat x0 x1 leaving 3 subgoals.
The subproof is completed by applying H0.
Apply nat_p_trans with
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply add_nat_com with
x0,
x1,
λ x3 x4 . add_nat x2 x0 ∈ x4 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_eeaa5555ccfaf9be2474522165cc658a4c21b3dcbef964c1d1aad1f792298727 with
x1,
x2,
x0 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H0.