Proofgold Proposition

∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 x3 . x1 x2 x3 ⟶ x1 x3 x2) ⟶ (∀ x2 . x2 ⊆ x0 ⟶ atleastp u3 x2 ⟶ not (∀ x3 . x3 ∈ x2 ⟶ ∀ x4 . x4 ∈ x2 ⟶ (x3 = x4 ⟶ ∀ x5 : ο . x5) ⟶ x1 x3 x4)) ⟶ (∀ x2 . x2 ⊆ x0 ⟶ atleastp u6 x2 ⟶ not (∀ x3 . x3 ∈ x2 ⟶ ∀ x4 . x4 ∈ x2 ⟶ (x3 = x4 ⟶ ∀ x5 : ο . x5) ⟶ not (x1 x3 x4))) ⟶ ∀ x2 x3 . nat_p x2 ⟶ ∀ x4 x5 . x5 ∈ DirGraphOutNeighbors x0 x1 x4 ⟶ ∀ x6 x7 x8 . x6 ⊆ x0 ⟶ x7 ⊆ x0 ⟶ x8 ⊆ x0 ⟶ x7 = setminus (DirGraphOutNeighbors x0 x1 x5) (Sing x4) ⟶ x8 = setminus {x10 ∈ setminus x0 (binunion (DirGraphOutNeighbors x0 x1 x4) (Sing x4))|equip (binintersect (DirGraphOutNeighbors x0 x1 x10) (DirGraphOutNeighbors x0 x1 x4)) x3} x7 ⟶ equip x6 x2 ⟶ (∀ x9 . x9 ∈ x6 ⟶ x9 = x5 ⟶ ∀ x10 : ο . x10) ⟶ (∀ x9 . x9 ∈ x6 ⟶ nIn x9 x7) ⟶ (∀ x9 . x9 ∈ x6 ⟶ nIn x9 x8) ⟶ (∀ x9 . x9 ∈ x6 ⟶ nIn x9 (DirGraphOutNeighbors x0 x1 x4)) ⟶ (∀ x9 . x9 ∈ x6 ⟶ nIn x9 (DirGraphOutNeighbors x0 x1 x5)) ⟶ (∀ x9 . x9 ∈ x6 ⟶ ∀ x10 . x10 ∈ x6 ⟶ (x9 = x10 ⟶ ∀ x11 : ο . x11) ⟶ ∀ x11 . x11 ∈ binintersect (DirGraphOutNeighbors x0 x1 x9) (DirGraphOutNeighbors x0 x1 x10) ⟶ x11 ∈ x6) ⟶ ∀ x9 : ι → ι . (∀ x10 . x10 ∈ x6 ⟶ x9 x10 ∈ x7) ⟶ (∀ x10 . x10 ∈ x6 ⟶ x1 x10 (x9 x10)) ⟶ (∀ x10 . x10 ∈ x7 ⟶ ∀ x11 : ο . (∀ x12 . and (x12 ∈ x6) (x9 x12 = x10) ⟶ x11) ⟶ x11) ⟶ (∀ x10 . x10 ∈ x8 ⟶ or (equip (binintersect (DirGraphOutNeighbors x0 x1 x10) (DirGraphOutNeighbors x0 x1 x5)) u1) (equip (binintersect (DirGraphOutNeighbors x0 x1 x10) (DirGraphOutNeighbors x0 x1 x5)) x3)) ⟶ equip {x10 ∈ setminus x0 (binunion (DirGraphOutNeighbors x0 x1 x5) (Sing x5))|equip (binintersect (DirGraphOutNeighbors x0 x1 x10) (DirGraphOutNeighbors x0 x1 x5)) u1} x2 ⟶ x8 ⊆ {x10 ∈ setminus x0 (binunion (DirGraphOutNeighbors x0 x1 x5) (Sing x5))|equip (binintersect (DirGraphOutNeighbors x0 x1 x10) (DirGraphOutNeighbors x0 x1 x5)) x3}

type
prop

theory
HotG

name
-

proof
PUQwi..

Megalodon
-

proofgold address
TMLgv..

creator
24141 Pr4zB../bf1ed..

owner
24142 Pr4zB../924b2..

term root
738c4..