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Proofgold Proof

pf
Let x0 of type ι → ι → ο be given.
Assume H0: ∀ x1 x2 . x0 x1 x2 ⟶ x0 x2 x1.
Assume H1: ∀ x1 . x1 ⊆ u18 ⟶ atleastp u3 x1 ⟶ not (∀ x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ (x2 = x3 ⟶ ∀ x4 : ο . x4) ⟶ x0 x2 x3).
Assume H2: ∀ x1 . x1 ⊆ u18 ⟶ atleastp u6 x1 ⟶ not (∀ x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ (x2 = x3 ⟶ ∀ x4 : ο . x4) ⟶ not (x0 x2 x3)).
Let x1 of type ι be given.
Assume H3: x1 ∈ u18.
Apply inj_linv with {x2 ∈ setminus u18 (binunion (DirGraphOutNeighbors u18 x0 x1) (Sing x1))|equip (binintersect (DirGraphOutNeighbors u18 x0 x2) (DirGraphOutNeighbors u18 x0 x1)) u1}, 4b3fa.. x0 x1.
Apply unknownprop_6dd97ca4d6a4f77c6a6f434ccf3fc69c1db75c2a4a9544712212da4fbeb74d93 with x0, x1 leaving 4 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.
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