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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: nat_p x0.
Assume H1: nat_p x1.
Assume H2: 1x0.
Assume H3: 1x1.
Claim L4: 0x0
Apply nat_trans with x0, 1, 0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying In_0_1.
Claim L5: 0x1
Apply nat_trans with x1, 1, 0 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
The subproof is completed by applying In_0_1.
Apply andI with x0mul_nat x0 x1, x1mul_nat x0 x1 leaving 2 subgoals.
Apply unknownprop_64298609228a1928dde1d66da0f04038e1112049f8f6469ec832eccc379525c0 with x0, x1 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying L4.
The subproof is completed by applying H3.
Apply mul_nat_com with x0, x1, λ x2 x3 . x1x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_64298609228a1928dde1d66da0f04038e1112049f8f6469ec832eccc379525c0 with x1, x0 leaving 4 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
The subproof is completed by applying L5.
The subproof is completed by applying H2.