| λ x0 x1 x2 . λ x3 x4 : ι → ι → ι . and (and (and (and (and (and (and (and (and (and (and (and (and (∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ x3 x5 x6 ∈ x0) (∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ x3 x5 (x3 x6 x7) = x3 (x3 x5 x6) x7)) (∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ x3 x5 x6 = x3 x6 x5)) (x1 ∈ x0)) (∀ x5 . x5 ∈ x0 ⟶ x3 x1 x5 = x5)) (∀ x5 . x5 ∈ x0 ⟶ ∀ x6 : ο . (∀ x7 . and (x7 ∈ x0) (x3 x5 x7 = x1) ⟶ x6) ⟶ x6)) (∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ x4 x5 x6 ∈ x0)) (∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ x4 x5 (x4 x6 x7) = x4 (x4 x5 x6) x7)) (x2 ∈ x0)) (x2 = x1 ⟶ ∀ x5 : ο . x5)) (∀ x5 . x5 ∈ x0 ⟶ x4 x2 x5 = x5)) (∀ x5 . x5 ∈ x0 ⟶ x4 x5 x2 = x5)) (∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ x4 x5 (x3 x6 x7) = x3 (x4 x5 x6) (x4 x5 x7))) (∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ x4 (x3 x5 x6) x7 = x3 (x4 x5 x7) (x4 x6 x7)) |
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| type |
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| ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → ο |
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| name |
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| explicit_Ring_with_id |
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