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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 bc82c.. x0 x1, x2, x3, λ x4 x5 . x5 = bc82c.. (bc82c.. x0 x2) (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.
The subproof is completed by applying H3.
Apply unknownprop_b2e39a9ed9d533304fc754b6d83e319e567a49123691e38b8c375068ad844b46 with x0, x1, x2, λ x4 x5 . bc82c.. x5 x3 = bc82c.. (bc82c.. x0 x2) (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.
Let x4 of type ιιο be given.
Apply unknownprop_d8f468fc749efab866c779febbe4cd601b5e2eeaa90e3f207f17de20f4ab68ab with bc82c.. x0 x2, x1, x3, λ x5 x6 . x4 x6 x5 leaving 3 subgoals.
Apply unknownprop_299d30a485627b811b1bc1069c06f437dd2ea8a2672044e2fbff59d7e1d539c2 with x0, x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H1.
The subproof is completed by applying H3.