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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: nat_p x0.
Let x1 of type ι be given.
Assume H1: nat_p x1.
Let x2 of type ι be given.
Assume H2: nat_p x2.
Assume H3: x1x2.
Apply add_nat_com with x0, x1, λ x3 x4 . x4add_nat x0 x2 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply add_nat_com with x0, x2, λ x3 x4 . add_nat x1 x0x4 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Apply unknownprop_0d6a07247642186ed37de81a1d03e639a8986da4b2779b46c2b8bfff453e4e37 with x1, x2, x0 leaving 4 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H0.