| ∀ x0 x1 : ι → ι → ι → ι → ο . (∀ x2 x3 x4 x5 . x0 x2 x3 x4 x5 ⟶ x0 x4 x5 x2 x3) ⟶ (∀ x2 . x2 ∈ u6 ⟶ ∀ x3 . x3 ∈ u6 ⟶ not (x0 x2 x3 x2 x3)) ⟶ (∀ x2 . x2 ∈ u6 ⟶ ∀ x3 . x3 ∈ u6 ⟶ x1 x2 x3 x2 x3) ⟶ (∀ x2 . x2 ∈ u6 ⟶ ∀ x3 . x3 ∈ u6 ⟶ ∀ x4 . x4 ∈ u6 ⟶ ∀ x5 . x5 ∈ u6 ⟶ (x2 = u5 ⟶ x3 = u5 ⟶ False) ⟶ (x4 = u5 ⟶ x5 = u5 ⟶ False) ⟶ x0 x2 x3 x4 x5 ⟶ x1 x2 x3 x4 x5) ⟶ (∀ x2 . x2 ∈ u6 ⟶ ∀ x3 . x3 ∈ u6 ⟶ ∀ x4 . x4 ∈ u6 ⟶ ∀ x5 . x5 ∈ u6 ⟶ (x2 = u5 ⟶ x3 = u5 ⟶ False) ⟶ (x4 = u5 ⟶ x5 = u5 ⟶ False) ⟶ (x2 = x4 ⟶ x3 = x5 ⟶ False) ⟶ x1 x2 x3 x4 x5 ⟶ x0 x2 x3 x4 x5) ⟶ (∀ x2 . x2 ∈ u6 ⟶ ∀ x3 . x3 ∈ u6 ⟶ ∀ x4 . x4 ∈ u6 ⟶ ∀ x5 . x5 ∈ u6 ⟶ ∀ x6 . x6 ∈ u6 ⟶ ∀ x7 . x7 ∈ u6 ⟶ ∀ x8 . x8 ∈ u6 ⟶ ∀ x9 . x9 ∈ u6 ⟶ x0 x2 x3 x4 x5 ⟶ x0 x2 x3 x6 x7 ⟶ x0 x2 x3 x8 x9 ⟶ x0 x4 x5 x6 x7 ⟶ x0 x4 x5 x8 x9 ⟶ x0 x6 x7 x8 x9 ⟶ False) ⟶ (∀ x2 . x2 ∈ u6 ⟶ ∀ x3 . x3 ∈ u6 ⟶ ∀ x4 . x4 ∈ u6 ⟶ ∀ x5 . x5 ∈ u6 ⟶ ∀ x6 . x6 ∈ u6 ⟶ ∀ x7 . x7 ∈ u6 ⟶ ∀ x8 . x8 ∈ u6 ⟶ ∀ x9 . x9 ∈ u6 ⟶ ∀ x10 . x10 ∈ u6 ⟶ ∀ x11 . x11 ∈ u6 ⟶ ∀ x12 . x12 ∈ u6 ⟶ ∀ x13 . x13 ∈ u6 ⟶ not (x1 x2 x3 x4 x5) ⟶ not (x1 x2 x3 x6 x7) ⟶ not (x1 x2 x3 x8 x9) ⟶ not (x1 x2 x3 x10 x11) ⟶ not (x1 x2 x3 x12 x13) ⟶ not (x1 x4 x5 x6 x7) ⟶ not (x1 x4 x5 x8 x9) ⟶ not (x1 x4 x5 x10 x11) ⟶ not (x1 x4 x5 x12 x13) ⟶ not (x1 x6 x7 x8 x9) ⟶ not (x1 x6 x7 x10 x11) ⟶ not (x1 x6 x7 x12 x13) ⟶ not (x1 x8 x9 x10 x11) ⟶ not (x1 x8 x9 x12 x13) ⟶ not (x1 x10 x11 x12 x13) ⟶ False) ⟶ not (TwoRamseyProp_atleastp u4 u6 (setminus (setprod u6 u6) (Sing (lam 2 (λ x2 . If_i (x2 = 0) u5 u5))))) |
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