Let x0 of type ι be given.

Assume H0: x0 ∈ u6.

Let x1 of type ι be given.

Assume H1: x1 ∈ u6.

Let x2 of type ι be given.

Assume H2: x2 ∈ u6.

Let x3 of type ι be given.

Assume H3: x3 ∈ u6.

Assume H4: TwoRamseyGraph_4_6_35_a x0 x1 x2 x3.

Apply unknownprop_e7f041280ca61a31be8a9ec6981da263e2b3464672b78681876510c023a0b883 with x0, x1, λ x4 x5 : ι → ι → ι → ι → ι → ι → ι . TwoRamseyGraph_4_6_Church6_squared_a (nth_6_tuple x0) x4 (nth_6_tuple x2) (nth_6_tuple (u6_squared_permutation__1_0_3_2_4_5__1_0_3_2_4_5__1_0_3_2_4_5__1_0_3_2_4_5__1_0_3_2_4_5__1_0_3_2_4_5 x2 x3)) = λ x6 x7 . x6 leaving 3 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H1.

Apply unknownprop_e7f041280ca61a31be8a9ec6981da263e2b3464672b78681876510c023a0b883 with x2, x3, λ x4 x5 : ι → ι → ι → ι → ι → ι → ι . TwoRamseyGraph_4_6_Church6_squared_a (nth_6_tuple x0) (Church6_squared_permutation__1_0_3_2_4_5__1_0_3_2_4_5__1_0_3_2_4_5__1_0_3_2_4_5__1_0_3_2_4_5__1_0_3_2_4_5 (nth_6_tuple x0) (nth_6_tuple x1)) (nth_6_tuple x2) x4 = λ x6 x7 . x6 leaving 3 subgoals.

The subproof is completed by applying H2.

The subproof is completed by applying H3.

Apply unknownprop_5343d24a197fc6ae088fd493f9cddb409896ab2759cba7d1f6bf8c6fbc2a1cfe with nth_6_tuple x0, nth_6_tuple x1, nth_6_tuple x2, nth_6_tuple x3 leaving 5 subgoals.

Apply unknownprop_90460311f4fb47844a8dd0d64a1306416f6a25ac4d465fc1811061f42791aace with x0.

The subproof is completed by applying H0.

Apply unknownprop_90460311f4fb47844a8dd0d64a1306416f6a25ac4d465fc1811061f42791aace with x1.

The subproof is completed by applying H1.

Apply unknownprop_90460311f4fb47844a8dd0d64a1306416f6a25ac4d465fc1811061f42791aace with x2.

The subproof is completed by applying H2.

Apply unknownprop_90460311f4fb47844a8dd0d64a1306416f6a25ac4d465fc1811061f42791aace with x3.

The subproof is completed by applying H3.

The subproof is completed by applying H4.

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Proofgold Proof