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Proofgold Proof

pf
Let x0 of type ιιο be given.
Assume H0: ∀ x1 x2 . x0 x1 x2x0 x2 x1.
Assume H1: ∀ x1 . x1u18atleastp u3 x1not (∀ x2 . x2x1∀ x3 . x3x1(x2 = x3∀ x4 : ο . x4)x0 x2 x3).
Assume H2: ∀ x1 . x1u18atleastp u6 x1not (∀ x2 . x2x1∀ x3 . x3x1(x2 = x3∀ x4 : ο . x4)not (x0 x2 x3)).
Let x1 of type ι be given.
Assume H3: x1u18.
Let x2 of type ι be given.
Apply unknownprop_dcc115a4b019991a4cb2500b43f932ed859900f80cfbe5a3e87503b346a0d594 with x0, x1, x2, f14ce.. x0 x1 x2binintersect (DirGraphOutNeighbors u18 x0 x2) (DirGraphOutNeighbors u18 x0 x1) leaving 6 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.
The subproof is completed by applying H4.
Assume H5: f14ce.. x0 x1 x2binintersect (DirGraphOutNeighbors u18 x0 x2) (DirGraphOutNeighbors u18 x0 x1).
Assume H6: f14ce.. x0 x1 x2 = 4b3fa.. x0 x1 x2∀ x3 : ο . x3.
The subproof is completed by applying H5.