Proofgold Asset

Param u6 : ι
Param TwoRamseyGraph_4_6_Church6_squared_b : (ι → ι → ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι → ι → ι) → (ι → ι → ι → ι → ι → ι → ι) → ι → ι → ι
Param nth_6_tuple : ι → ι → ι → ι → ι → ι → ι → ι
Definition TwoRamseyGraph_4_6_35_b := λ x0 x1 x2 x3 . x0 ∈ u6 ⟶ x1 ∈ u6 ⟶ x2 ∈ u6 ⟶ x3 ∈ u6 ⟶ TwoRamseyGraph_4_6_Church6_squared_b (nth_6_tuple x0) (nth_6_tuple x1) (nth_6_tuple x2) (nth_6_tuple x3) = λ x5 x6 . x5
Param Church6_p : (ι → ι → ι → ι → ι → ι → ι) → ο
Param Church6_to_u6 : CT6 ι
Known 17ae2.. : ∀ x0 . x0 ∈ u6 ⟶ ∀ x1 : ο . (∀ x2 : ι → ι → ι → ι → ι → ι → ι . Church6_p x2 ⟶ x0 = Church6_to_u6 x2 ⟶ x1) ⟶ x1
Known 3ac64.. : ∀ x0 : ι → ι → ι → ι → ι → ι → ι . Church6_p x0 ⟶ nth_6_tuple (Church6_to_u6 x0) = x0
Known 63562.. : ∀ x0 x1 x2 x3 : ι → ι → ι → ι → ι → ι → ι . Church6_p x0 ⟶ Church6_p x1 ⟶ Church6_p x2 ⟶ Church6_p x3 ⟶ (TwoRamseyGraph_4_6_Church6_squared_b x0 x1 x2 x3 = λ x5 x6 . x5) ⟶ TwoRamseyGraph_4_6_Church6_squared_b x2 x3 x0 x1 = λ x5 x6 . x5
Theorem a3e36.. : ∀ x0 x1 x2 x3 . TwoRamseyGraph_4_6_35_b x0 x1 x2 x3 ⟶ TwoRamseyGraph_4_6_35_b x2 x3 x0 x1 (proof)