Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Apply unknownprop_4c4a30cb28bcd21744eec16e4ab4637f15035a845cbbb0ffbe052be5f3b1352d with
x0,
TwoRamseyGraph_4_6_Church6_squared_b (nth_6_tuple x2) (nth_6_tuple x3) (nth_6_tuple x0) (nth_6_tuple x1) = λ x4 x5 . x4 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x4 of type ι → ι → ι → ι → ι → ι → ι be given.
Apply unknownprop_4c4a30cb28bcd21744eec16e4ab4637f15035a845cbbb0ffbe052be5f3b1352d with
x1,
TwoRamseyGraph_4_6_Church6_squared_b (nth_6_tuple x2) (nth_6_tuple x3) (nth_6_tuple x0) (nth_6_tuple x1) = λ x5 x6 . x5 leaving 2 subgoals.
The subproof is completed by applying H1.
Let x5 of type ι → ι → ι → ι → ι → ι → ι be given.
Apply H10 with
λ x6 x7 . TwoRamseyGraph_4_6_Church6_squared_b (nth_6_tuple x2) (nth_6_tuple x3) (nth_6_tuple x7) (nth_6_tuple x1) = λ x8 x9 . x8.
Apply H12 with
λ x6 x7 . TwoRamseyGraph_4_6_Church6_squared_b (nth_6_tuple x2) (nth_6_tuple x3) (nth_6_tuple (Church6_to_u6 x4)) (nth_6_tuple x7) = λ x8 x9 . x8.
Apply unknownprop_1df6cb25245842ac80f846f984ad1ab224979cc48aebddb9e27917721a4b0bdb with
x4,
λ x6 x7 : ι → ι → ι → ι → ι → ι → ι . TwoRamseyGraph_4_6_Church6_squared_b (nth_6_tuple x2) (nth_6_tuple x3) x7 (nth_6_tuple (Church6_to_u6 x5)) = λ x8 x9 . x8 leaving 2 subgoals.
The subproof is completed by applying H9.
Apply unknownprop_1df6cb25245842ac80f846f984ad1ab224979cc48aebddb9e27917721a4b0bdb with
x5,
λ x6 x7 : ι → ι → ι → ι → ι → ι → ι . TwoRamseyGraph_4_6_Church6_squared_b (nth_6_tuple x2) (nth_6_tuple x3) x4 x7 = λ x8 x9 . x8 leaving 2 subgoals.
The subproof is completed by applying H11.
Apply unknownprop_4c4a30cb28bcd21744eec16e4ab4637f15035a845cbbb0ffbe052be5f3b1352d with
x2,
TwoRamseyGraph_4_6_Church6_squared_b (nth_6_tuple x2) (nth_6_tuple x3) x4 x5 = λ x6 x7 . x6 leaving 2 subgoals.
The subproof is completed by applying H2.
Let x6 of type ι → ι → ι → ι → ι → ι → ι be given.
Apply unknownprop_4c4a30cb28bcd21744eec16e4ab4637f15035a845cbbb0ffbe052be5f3b1352d with
x3,
TwoRamseyGraph_4_6_Church6_squared_b (nth_6_tuple x2) (nth_6_tuple x3) x4 x5 = λ x7 x8 . x7 leaving 2 subgoals.
The subproof is completed by applying H3.
Let x7 of type ι → ι → ι → ι → ι → ι → ι be given.
Apply H14 with
λ x8 x9 . TwoRamseyGraph_4_6_Church6_squared_b (nth_6_tuple x9) (nth_6_tuple x3) x4 x5 = λ x10 x11 . x10.
Apply H16 with
λ x8 x9 . TwoRamseyGraph_4_6_Church6_squared_b (nth_6_tuple (Church6_to_u6 x6)) (nth_6_tuple x9) x4 x5 = λ x10 x11 . x10.
Apply unknownprop_1df6cb25245842ac80f846f984ad1ab224979cc48aebddb9e27917721a4b0bdb with
x6,
λ x8 x9 : ι → ι → ι → ι → ι → ι → ι . TwoRamseyGraph_4_6_Church6_squared_b x9 (nth_6_tuple (Church6_to_u6 x7)) x4 x5 = λ x10 x11 . x10 leaving 2 subgoals.
The subproof is completed by applying H13.
Apply unknownprop_1df6cb25245842ac80f846f984ad1ab224979cc48aebddb9e27917721a4b0bdb with
x7,
λ x8 x9 : ι → ι → ι → ι → ι → ι → ι . TwoRamseyGraph_4_6_Church6_squared_b x6 x9 x4 x5 = λ x10 x11 . x10 leaving 2 subgoals.
The subproof is completed by applying H15.
Apply unknownprop_a6b94d39e112543346fd3d628055520b18b2a8c0ff7c088a719d9dfd3d3e8e01 with
x4,
x5,
x6,
x7 leaving 5 subgoals.
The subproof is completed by applying H9.
The subproof is completed by applying H11.
The subproof is completed by applying H13.
The subproof is completed by applying H15.
Apply unknownprop_1df6cb25245842ac80f846f984ad1ab224979cc48aebddb9e27917721a4b0bdb with
x4,
λ x8 x9 : ι → ι → ι → ι → ι → ι → ι . TwoRamseyGraph_4_6_Church6_squared_b x8 x5 x6 x7 = λ x10 x11 . x10 leaving 2 subgoals.
The subproof is completed by applying H9.