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Proofgold Signed Transaction

vin
Pr7sm../29691..
PUa88../a8dcd..
vout
Pr7sm../63b05.. 5.76 bars
TMKW3../b5612.. ownership of 6ea7a.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
TMMcg../f5147.. ownership of d6a8e.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
PUQvm../b26b8.. 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 2de86.. := 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 ⟶ not (x0 x3 x6) ⟶ x0 x4 x6 ⟶ not (x0 x5 x6) ⟶ x7) ⟶ x7
Definition 21422.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (2de86.. 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 ⟶ not (x0 x4 x7) ⟶ not (x0 x5 x7) ⟶ x0 x6 x7 ⟶ x8) ⟶ x8
Definition f0d5b.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (21422.. 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 a4abc.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (f0d5b.. 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) ⟶ 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 03a93.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (a4abc.. 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 ⟶ x0 x2 x10 ⟶ x0 x3 x10 ⟶ x0 x4 x10 ⟶ not (x0 x5 x10) ⟶ not (x0 x6 x10) ⟶ not (x0 x7 x10) ⟶ not (x0 x8 x10) ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition b019a.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (a4abc.. 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) ⟶ x0 x6 x10 ⟶ not (x0 x7 x10) ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition 04c7a.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (b019a.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ x0 x1 x11 ⟶ x0 x2 x11 ⟶ x0 x3 x11 ⟶ x0 x4 x11 ⟶ not (x0 x5 x11) ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ not (x0 x8 x11) ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition 62523.. := 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) ⟶ not (x0 x3 x5) ⟶ x0 x4 x5 ⟶ x6) ⟶ x6
Definition a542b.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (62523.. 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) ⟶ not (x0 x2 x6) ⟶ x0 x3 x6 ⟶ not (x0 x4 x6) ⟶ x0 x5 x6 ⟶ x7) ⟶ x7
Definition 2fb86.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (a542b.. 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 14b71.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2fb86.. 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 286f8.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (14b71.. 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 ⟶ not (x0 x8 x9) ⟶ x10) ⟶ x10
Definition 68d0b.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (286f8.. 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 ⟶ x0 x2 x10 ⟶ x0 x3 x10 ⟶ x0 x4 x10 ⟶ not (x0 x5 x10) ⟶ not (x0 x6 x10) ⟶ not (x0 x7 x10) ⟶ not (x0 x8 x10) ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition 7e591.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (68d0b.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ x0 x1 x11 ⟶ not (x0 x2 x11) ⟶ not (x0 x3 x11) ⟶ x0 x4 x11 ⟶ not (x0 x5 x11) ⟶ x0 x6 x11 ⟶ not (x0 x7 x11) ⟶ x0 x8 x11 ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition aa284.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (03a93.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ x0 x1 x11 ⟶ not (x0 x2 x11) ⟶ not (x0 x3 x11) ⟶ not (x0 x4 x11) ⟶ not (x0 x5 x11) ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ x0 x8 x11 ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition 36d58.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (2de86.. 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 af16d.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (36d58.. 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 a3794.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (af16d.. 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) ⟶ x0 x3 x9 ⟶ not (x0 x4 x9) ⟶ not (x0 x5 x9) ⟶ x0 x6 x9 ⟶ not (x0 x7 x9) ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition 6f07c.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (a3794.. 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 ⟶ x0 x2 x10 ⟶ not (x0 x3 x10) ⟶ not (x0 x4 x10) ⟶ x0 x5 x10 ⟶ not (x0 x6 x10) ⟶ not (x0 x7 x10) ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition 0e688.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (6f07c.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ not (x0 x1 x11) ⟶ x0 x2 x11 ⟶ not (x0 x3 x11) ⟶ not (x0 x4 x11) ⟶ not (x0 x5 x11) ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ x0 x8 x11 ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition 796c4.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (2de86.. 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 ⟶ not (x0 x4 x7) ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8
Definition d7cce.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (796c4.. 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 f7902.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (d7cce.. 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) ⟶ x0 x2 x9 ⟶ not (x0 x3 x9) ⟶ not (x0 x4 x9) ⟶ x0 x5 x9 ⟶ not (x0 x6 x9) ⟶ x0 x7 x9 ⟶ x0 x8 x9 ⟶ x10) ⟶ x10
Definition 856bc.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (f7902.. 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 913ca.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (856bc.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ x0 x1 x11 ⟶ x0 x2 x11 ⟶ x0 x3 x11 ⟶ not (x0 x4 x11) ⟶ not (x0 x5 x11) ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ x0 x8 x11 ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition ca8ce.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (f7902.. 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) ⟶ x0 x5 x10 ⟶ x0 x6 x10 ⟶ not (x0 x7 x10) ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition d10a3.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (ca8ce.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ x0 x1 x11 ⟶ x0 x2 x11 ⟶ x0 x3 x11 ⟶ not (x0 x4 x11) ⟶ not (x0 x5 x11) ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ x0 x8 x11 ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition f8fdb.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (a3794.. 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) ⟶ not (x0 x1 x10) ⟶ x0 x2 x10 ⟶ not (x0 x3 x10) ⟶ not (x0 x4 x10) ⟶ not (x0 x5 x10) ⟶ not (x0 x6 x10) ⟶ x0 x7 x10 ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition c34cb.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (f8fdb.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ x0 x1 x11 ⟶ x0 x2 x11 ⟶ not (x0 x3 x11) ⟶ not (x0 x4 x11) ⟶ not (x0 x5 x11) ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ x0 x8 x11 ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
Definition 84d91.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (d7cce.. 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 66dda.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (84d91.. 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) ⟶ not (x0 x1 x10) ⟶ x0 x2 x10 ⟶ not (x0 x3 x10) ⟶ not (x0 x4 x10) ⟶ not (x0 x5 x10) ⟶ not (x0 x6 x10) ⟶ x0 x7 x10 ⟶ x0 x8 x10 ⟶ not (x0 x9 x10) ⟶ x11) ⟶ x11
Definition 805ab.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (66dda.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 ⟶ (x1 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x2 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x3 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x4 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x5 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x6 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x7 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x8 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x9 = x11 ⟶ ∀ x13 : ο . x13) ⟶ (x10 = x11 ⟶ ∀ x13 : ο . x13) ⟶ x0 x1 x11 ⟶ x0 x2 x11 ⟶ x0 x3 x11 ⟶ not (x0 x4 x11) ⟶ not (x0 x5 x11) ⟶ not (x0 x6 x11) ⟶ not (x0 x7 x11) ⟶ x0 x8 x11 ⟶ not (x0 x9 x11) ⟶ not (x0 x10 x11) ⟶ x12) ⟶ x12
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 8335d.. : ∀ 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 ⟶ ∀ x13 . x13 ∈ x0 ⟶ 03a93.. x2 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ ∀ x14 : ο . (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ not (x2 x11 x3) ⟶ not (x2 x12 x3) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ x2 x5 x3 ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ not (x2 x11 x3) ⟶ not (x2 x12 x3) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ x2 x9 x3 ⟶ not (x2 x10 x3) ⟶ not (x2 x11 x3) ⟶ not (x2 x12 x3) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ not (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) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ x2 x5 x3 ⟶ not (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) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (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) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (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) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (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) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (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) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ not (x2 x12 x3) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ x2 x5 x3 ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ not (x2 x9 x3) ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ not (x2 x12 x3) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ not (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) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (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) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (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) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ (x2 x4 x3 ⟶ not (x2 x5 x3) ⟶ not (x2 x6 x3) ⟶ not (x2 x7 x3) ⟶ x2 x8 x3 ⟶ x2 x9 x3 ⟶ not (x2 x10 x3) ⟶ x2 x11 x3 ⟶ not (x2 x12 x3) ⟶ not (x2 x13 x3) ⟶ x14) ⟶ x14
Known d257b.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ⟶ x1 x3 x2) ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ 8b6ad.. x1 x2 x3 x4 x5 ⟶ 8b6ad.. x1 x3 x4 x2 x5
Known neq_i_symneq_i_sym : ∀ x0 x1 . (x0 = x1 ⟶ ∀ x2 : ο . x2) ⟶ x1 = x0 ⟶ ∀ x2 : ο . x2
Known 19497.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ⟶ x1 x3 x2) ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ ∀ x10 . x10 ∈ x0 ⟶ ∀ x11 . x11 ∈ x0 ⟶ 03a93.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 ⟶ 03a93.. x1 x9 x7 x6 x11 x4 x3 x10 x2 x8 x5
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 6ea7a.. : ∀ 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 ⟶ ∀ x13 . x13 ∈ x0 ⟶ 03a93.. x2 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ ∀ x14 : ο . (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 04c7a.. x2 x15 x16 x3 x17 x18 x19 x20 x21 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 04c7a.. x2 x15 x16 x17 x18 x19 x20 x21 x22 x23 x3 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 7e591.. x2 x15 x16 x17 x18 x19 x20 x21 x3 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ aa284.. x2 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x3 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 0e688.. x2 x15 x16 x17 x18 x3 x19 x20 x21 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 913ca.. x2 x15 x16 x17 x18 x3 x19 x20 x21 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ d10a3.. x2 x15 x16 x17 x18 x3 x19 x20 x21 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ c34cb.. x2 x3 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 ⟶ x14) ⟶ (∀ x15 . x15 ∈ x0 ⟶ ∀ x16 . x16 ∈ x0 ⟶ ∀ x17 . x17 ∈ x0 ⟶ ∀ x18 . x18 ∈ x0 ⟶ ∀ x19 . x19 ∈ x0 ⟶ ∀ x20 . x20 ∈ x0 ⟶ ∀ x21 . x21 ∈ x0 ⟶ ∀ x22 . x22 ∈ x0 ⟶ ∀ x23 . x23 ∈ x0 ⟶ ∀ x24 . x24 ∈ x0 ⟶ 805ab.. x2 x15 x16 x17 x18 x3 x19 x20 x21 x22 x23 x24 ⟶ x14) ⟶ x14 (proof)