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Pr3UG../540c6.. 12.39 barsTMUuJ../b21de.. ownership of 7a527.. as prop with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0TMRAQ../438ba.. ownership of d15cc.. as prop with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0PURoa../16447.. doc published by Pr4zB..Param ba9c9.. : (ι → ι → ο) → ι → ι → ι → ι → ι → ι → ι → οParam notnot : ο → οDefinition 70101.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (ba9c9.. 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) ⟶ x0 x3 x8 ⟶ not (x0 x4 x8) ⟶ not (x0 x5 x8) ⟶ not (x0 x6 x8) ⟶ not (x0 x7 x8) ⟶ x9) ⟶ x9Known 57c5c.. : ∀ 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 ⟶ ba9c9.. x1 x2 x3 x4 x5 x6 x7 x8 ⟶ ba9c9.. x1 x3 x2 x4 x5 x6 x8 x7Theorem 7a527.. : ∀ 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 ⟶ 70101.. x1 x2 x3 x4 x5 x6 x7 x8 x9 ⟶ 70101.. x1 x3 x2 x4 x5 x6 x8 x7 x9 (proof) |
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