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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 ι be given.
Assume H0: 80242.. x0.
Assume H1: 80242.. x1.
Assume H2: 80242.. x2.
Assume H3: 099f3.. x0 (bc82c.. x2 x1).
Apply unknownprop_36f11cc7571fa2487251d5a7c42936b64e63f594759a4c4f588173d9cd2aec53 with bc82c.. x0 (f4dc0.. x1), x1, x2 leaving 4 subgoals.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with x0, f4dc0.. x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_8fbd0c2b48e78882e15936a0ad5f4a3c5af2cb37d9320d8cb210a91462e202ca with x1.
The subproof is completed by applying H1.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply unknownprop_d8f468fc749efab866c779febbe4cd601b5e2eeaa90e3f207f17de20f4ab68ab with x0, f4dc0.. x1, x1, λ x3 x4 . 099f3.. x3 (bc82c.. x2 x1) leaving 4 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_8fbd0c2b48e78882e15936a0ad5f4a3c5af2cb37d9320d8cb210a91462e202ca with x1.
The subproof is completed by applying H1.
The subproof is completed by applying H1.
Apply unknownprop_e9028cba89e89a77a2997386e65c0b630a8780de144826d2529038cff74afa4d with x1, λ x3 x4 . 099f3.. (bc82c.. x0 x4) (bc82c.. x2 x1) leaving 2 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_3201a7f403ac32d9752260880c29e9f9084a9b6a0cf9218208744c4c82940cb1 with x0, λ x3 x4 . 099f3.. x4 (bc82c.. x2 x1) leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.