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Proofgold Signed Transaction

vin
PrCit../1dd85..
PUSPG../faf82..
vout
PrCit../5b94e.. 3.04 bars
TMTv8../81023.. ownership of ab4e4.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
TMP45../2045c.. ownership of 93db9.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
PUeVq../5089b.. doc published by Pr4zB..
Param 4402e.. : ι → (ι → ι → ο) → ο
Param cf2df.. : ι → (ι → ι → ο) → ο
Definition SubqSubq := λ x0 x1 . ∀ x2 . x2 ∈ x0 ⟶ x2 ∈ x1
Param setminussetminus : ι → ι → ι
Param SingSing : ι → ι
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0 ⟶ False
Definition 8b6ad.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 . ∀ x5 : ο . ((x1 = x2 ⟶ ∀ x6 : ο . x6) ⟶ (x1 = x3 ⟶ ∀ x6 : ο . x6) ⟶ (x2 = x3 ⟶ ∀ x6 : ο . x6) ⟶ (x1 = x4 ⟶ ∀ x6 : ο . x6) ⟶ (x2 = x4 ⟶ ∀ x6 : ο . x6) ⟶ (x3 = x4 ⟶ ∀ x6 : ο . x6) ⟶ not (x0 x1 x2) ⟶ not (x0 x1 x3) ⟶ not (x0 x2 x3) ⟶ not (x0 x1 x4) ⟶ not (x0 x2 x4) ⟶ not (x0 x3 x4) ⟶ x5) ⟶ x5
Definition c5756.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 . ∀ x6 : ο . (8b6ad.. x0 x1 x2 x3 x4 ⟶ (x1 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x2 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x3 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x4 = x5 ⟶ ∀ x7 : ο . x7) ⟶ not (x0 x1 x5) ⟶ not (x0 x2 x5) ⟶ x0 x3 x5 ⟶ x0 x4 x5 ⟶ x6) ⟶ x6
Definition 4ce91.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (c5756.. x0 x1 x2 x3 x4 x5 ⟶ (x1 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x6 ⟶ ∀ x8 : ο . x8) ⟶ x0 x1 x6 ⟶ x0 x2 x6 ⟶ not (x0 x3 x6) ⟶ not (x0 x4 x6) ⟶ not (x0 x5 x6) ⟶ x7) ⟶ x7
Definition cb525.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (4ce91.. x0 x1 x2 x3 x4 x5 x6 ⟶ (x1 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x0 x1 x7 ⟶ x0 x2 x7 ⟶ x0 x3 x7 ⟶ x0 x4 x7 ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition 11c17.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (cb525.. x0 x1 x2 x3 x4 x5 x6 x7 ⟶ (x1 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ not (x0 x1 x8) ⟶ not (x0 x2 x8) ⟶ not (x0 x3 x8) ⟶ x0 x4 x8 ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition 9069f.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (11c17.. x0 x1 x2 x3 x4 x5 x6 x7 x8 ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ x0 x1 x9 ⟶ x0 x2 x9 ⟶ not (x0 x3 x9) ⟶ not (x0 x4 x9) ⟶ x0 x5 x9 ⟶ not (x0 x6 x9) ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition f8709.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (c5756.. x0 x1 x2 x3 x4 x5 ⟶ (x1 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x6 ⟶ ∀ x8 : ο . x8) ⟶ not (x0 x1 x6) ⟶ x0 x2 x6 ⟶ x0 x3 x6 ⟶ x0 x4 x6 ⟶ not (x0 x5 x6) ⟶ x7) ⟶ x7
Definition 16c0f.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (f8709.. x0 x1 x2 x3 x4 x5 x6 ⟶ (x1 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x0 x1 x7 ⟶ x0 x2 x7 ⟶ not (x0 x3 x7) ⟶ x0 x4 x7 ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition cc0ce.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (16c0f.. x0 x1 x2 x3 x4 x5 x6 x7 ⟶ (x1 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ not (x0 x1 x8) ⟶ x0 x2 x8 ⟶ not (x0 x3 x8) ⟶ not (x0 x4 x8) ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition 70a3c.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (cc0ce.. x0 x1 x2 x3 x4 x5 x6 x7 x8 ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ x0 x1 x9 ⟶ not (x0 x2 x9) ⟶ not (x0 x3 x9) ⟶ not (x0 x4 x9) ⟶ not (x0 x5 x9) ⟶ x0 x6 x9 ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition f982a.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (70a3c.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ x0 x1 x10 ⟶ not (x0 x2 x10) ⟶ x0 x3 x10 ⟶ x0 x4 x10 ⟶ not (x0 x5 x10) ⟶ not (x0 x6 x10) ⟶ not (x0 x7 x10) ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition 27260.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (f8709.. x0 x1 x2 x3 x4 x5 x6 ⟶ (x1 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x0 x1 x7 ⟶ x0 x2 x7 ⟶ not (x0 x3 x7) ⟶ not (x0 x4 x7) ⟶ x0 x5 x7 ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition dfcf9.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (27260.. x0 x1 x2 x3 x4 x5 x6 x7 ⟶ (x1 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ not (x0 x1 x8) ⟶ x0 x2 x8 ⟶ not (x0 x3 x8) ⟶ not (x0 x4 x8) ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition 8d9b1.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (dfcf9.. x0 x1 x2 x3 x4 x5 x6 x7 x8 ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ x0 x1 x9 ⟶ not (x0 x2 x9) ⟶ not (x0 x3 x9) ⟶ not (x0 x4 x9) ⟶ not (x0 x5 x9) ⟶ x0 x6 x9 ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition 5c669.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (8d9b1.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ x0 x1 x10 ⟶ not (x0 x2 x10) ⟶ x0 x3 x10 ⟶ x0 x4 x10 ⟶ not (x0 x5 x10) ⟶ not (x0 x6 x10) ⟶ not (x0 x7 x10) ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition 2b028.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 . ∀ x6 : ο . (8b6ad.. x0 x1 x2 x3 x4 ⟶ (x1 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x2 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x3 = x5 ⟶ ∀ x7 : ο . x7) ⟶ (x4 = x5 ⟶ ∀ x7 : ο . x7) ⟶ not (x0 x1 x5) ⟶ x0 x2 x5 ⟶ x0 x3 x5 ⟶ x0 x4 x5 ⟶ x6) ⟶ x6
Definition 9ab39.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (2b028.. x0 x1 x2 x3 x4 x5 ⟶ (x1 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x2 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x3 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x4 = x6 ⟶ ∀ x8 : ο . x8) ⟶ (x5 = x6 ⟶ ∀ x8 : ο . x8) ⟶ not (x0 x1 x6) ⟶ x0 x2 x6 ⟶ x0 x3 x6 ⟶ x0 x4 x6 ⟶ not (x0 x5 x6) ⟶ x7) ⟶ x7
Definition 468d8.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (9ab39.. x0 x1 x2 x3 x4 x5 x6 ⟶ (x1 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x0 x1 x7 ⟶ not (x0 x2 x7) ⟶ x0 x3 x7 ⟶ x0 x4 x7 ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition 3b6e0.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (468d8.. x0 x1 x2 x3 x4 x5 x6 x7 ⟶ (x1 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ not (x0 x1 x8) ⟶ not (x0 x2 x8) ⟶ not (x0 x3 x8) ⟶ x0 x4 x8 ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition 6e051.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (3b6e0.. x0 x1 x2 x3 x4 x5 x6 x7 x8 ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ x0 x1 x9 ⟶ not (x0 x2 x9) ⟶ not (x0 x3 x9) ⟶ not (x0 x4 x9) ⟶ x0 x5 x9 ⟶ x0 x6 x9 ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition 0809e.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (6e051.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ x0 x1 x10 ⟶ not (x0 x2 x10) ⟶ x0 x3 x10 ⟶ not (x0 x4 x10) ⟶ not (x0 x5 x10) ⟶ not (x0 x6 x10) ⟶ not (x0 x7 x10) ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition 182cc.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (f8709.. x0 x1 x2 x3 x4 x5 x6 ⟶ (x1 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x2 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x3 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x4 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x5 = x7 ⟶ ∀ x9 : ο . x9) ⟶ (x6 = x7 ⟶ ∀ x9 : ο . x9) ⟶ x0 x1 x7 ⟶ x0 x2 x7 ⟶ not (x0 x3 x7) ⟶ not (x0 x4 x7) ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition 84d5a.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (182cc.. x0 x1 x2 x3 x4 x5 x6 x7 ⟶ (x1 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x2 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x3 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x4 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x5 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x6 = x8 ⟶ ∀ x10 : ο . x10) ⟶ (x7 = x8 ⟶ ∀ x10 : ο . x10) ⟶ not (x0 x1 x8) ⟶ x0 x2 x8 ⟶ not (x0 x3 x8) ⟶ not (x0 x4 x8) ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9
Definition 2e1d5.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (84d5a.. x0 x1 x2 x3 x4 x5 x6 x7 x8 ⟶ (x1 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x2 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x3 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x4 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x5 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x6 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x7 = x9 ⟶ ∀ x11 : ο . x11) ⟶ (x8 = x9 ⟶ ∀ x11 : ο . x11) ⟶ not (x0 x1 x9) ⟶ not (x0 x2 x9) ⟶ x0 x3 x9 ⟶ x0 x4 x9 ⟶ not (x0 x5 x9) ⟶ not (x0 x6 x9) ⟶ x0 x7 x9 ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition d833d.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (2e1d5.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ (x1 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x2 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x3 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x4 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x5 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x6 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x7 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x8 = x10 ⟶ ∀ x12 : ο . x12) ⟶ (x9 = x10 ⟶ ∀ x12 : ο . x12) ⟶ x0 x1 x10 ⟶ not (x0 x2 x10) ⟶ not (x0 x3 x10) ⟶ not (x0 x4 x10) ⟶ not (x0 x5 x10) ⟶ x0 x6 x10 ⟶ not (x0 x7 x10) ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition andand := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2
Definition nInnIn := λ x0 x1 . not (x0 ∈ x1)
Known setminusEsetminusE : ∀ x0 x1 x2 . x2 ∈ setminus x0 x1 ⟶ and (x2 ∈ x0) (nIn x2 x1)
Known 0d6e6.. : ∀ x0 x1 . ∀ x2 : ι → ι → ο . (∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ x2 x3 x4 ⟶ x2 x4 x3) ⟶ 4402e.. x1 x2 ⟶ cf2df.. x1 x2 ⟶ ∀ x3 . x3 ∈ x1 ⟶ x0 ⊆ setminus x1 (Sing x3) ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ 9069f.. x2 x4 x5 x6 x7 x8 x9 x10 x11 x12 ⟶ ∀ x13 : ο . (not (x2 x4 x3) ⟶ not (x2 x5 x3) ⟶ x2 x6 x3 ⟶ not (x2 x7 x3) ⟶ not (x2 x8 x3) ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ not (x2 x12 x3) ⟶ x13) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ x2 x6 x3 ⟶ not (x2 x7 x3) ⟶ not (x2 x8 x3) ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ not (x2 x12 x3) ⟶ x13) ⟶ (not (x2 x4 x3) ⟶ x2 x5 x3 ⟶ x2 x6 x3 ⟶ not (x2 x7 x3) ⟶ not (x2 x8 x3) ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ not (x2 x12 x3) ⟶ x13) ⟶ (x2 x4 x3 ⟶ x2 x5 x3 ⟶ x2 x6 x3 ⟶ not (x2 x7 x3) ⟶ not (x2 x8 x3) ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ not (x2 x12 x3) ⟶ x13) ⟶ (not (x2 x4 x3) ⟶ not (x2 x5 x3) ⟶ x2 x6 x3 ⟶ not (x2 x7 x3) ⟶ not (x2 x8 x3) ⟶ x2 x9 x3 ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ not (x2 x12 x3) ⟶ x13) ⟶ x13
Known neq_i_symneq_i_sym : ∀ x0 x1 . (x0 = x1 ⟶ ∀ x2 : ο . x2) ⟶ x1 = x0 ⟶ ∀ x2 : ο . x2
Known Subq_traSubq_tra : ∀ x0 x1 x2 . x0 ⊆ x1 ⟶ x1 ⊆ x2 ⟶ x0 ⊆ x2
Known setminus_Subqsetminus_Subq : ∀ x0 x1 . setminus x0 x1 ⊆ x0
Known SingISingI : ∀ x0 . x0 ∈ Sing x0
Theorem ab4e4.. : ∀ x0 x1 . ∀ x2 : ι → ι → ο . (∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ x2 x3 x4 ⟶ x2 x4 x3) ⟶ 4402e.. x1 x2 ⟶ cf2df.. x1 x2 ⟶ ∀ x3 . x3 ∈ x1 ⟶ x0 ⊆ setminus x1 (Sing x3) ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ 9069f.. x2 x4 x5 x6 x7 x8 x9 x10 x11 x12 ⟶ ∀ x13 : ο . (∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ f982a.. x2 x14 x15 x16 x17 x18 x19 x3 x20 x21 x22 ⟶ x13) ⟶ (∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ 5c669.. x2 x14 x15 x16 x17 x18 x19 x3 x20 x21 x22 ⟶ x13) ⟶ (∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ 0809e.. x2 x14 x15 x16 x3 x17 x18 x19 x20 x21 x22 ⟶ x13) ⟶ (∀ x14 . x14 ∈ x0 ⟶ ∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ d833d.. x2 x3 x14 x15 x16 x17 x18 x19 x20 x21 x22 ⟶ x13) ⟶ x13 (proof)