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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ιι be given.
Let x3 of type ι be given.
Assume H0: x0 = 8eacd.. x1 x2 x3.
Let x4 of type ι be given.
Assume H1: prim1 x4 x1.
Apply H0 with λ x5 x6 . x2 x4 = f482f.. (f482f.. x6 (4ae4a.. 4a7ef..)) x4.
Apply unknownprop_d7d39a6ae9dd573b529ad4d558553a3d5dfa88cfa249f628a74ae5b338307a3e with x1, 0fc90.. x1 x2, x3, λ x5 x6 . x2 x4 = f482f.. x6 x4.
Let x5 of type ιιο be given.
Apply unknownprop_b456609235d152f08bccfce314d541d7c44f3716137c00b0ce21cf467ba83d17 with x1, x2, x4, λ x6 x7 . x5 x7 x6.
The subproof is completed by applying H1.