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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.
Let x3 of type ι be given.
Assume H0: 80242.. x0.
Assume H1: 80242.. x1.
Assume H2: 80242.. x2.
Assume H3: 80242.. x3.
Apply unknownprop_d8f468fc749efab866c779febbe4cd601b5e2eeaa90e3f207f17de20f4ab68ab with x0, x1, x2, λ x4 x5 . bc82c.. x5 (bc82c.. (f4dc0.. x2) x3) = bc82c.. x0 (bc82c.. x1 x3) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply unknownprop_d8f468fc749efab866c779febbe4cd601b5e2eeaa90e3f207f17de20f4ab68ab with bc82c.. x0 x1, x2, bc82c.. (f4dc0.. x2) x3, λ x4 x5 . x4 = bc82c.. x0 (bc82c.. x1 x3) leaving 4 subgoals.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with f4dc0.. x2, x3 leaving 2 subgoals.
Apply unknownprop_8fbd0c2b48e78882e15936a0ad5f4a3c5af2cb37d9320d8cb210a91462e202ca with x2.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply unknownprop_87e2f2edbfc1171dfd16856d2222fe54a683af6a605ab4e98a195ae66b501172 with x2, x3, λ x4 x5 . bc82c.. (bc82c.. x0 x1) x5 = bc82c.. x0 (bc82c.. x1 x3) leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Let x4 of type ιιο be given.
Apply unknownprop_d8f468fc749efab866c779febbe4cd601b5e2eeaa90e3f207f17de20f4ab68ab with x0, x1, x3, λ x5 x6 . x4 x6 x5 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H3.