Let x0 of type ι → ι → ι → ι → ι → ι → ι be given.
Let x1 of type ι → ι → ι → ι → ι → ι → ι be given.
Let x2 of type ι → ι → ι → ι → ι → ι → ι be given.
Let x3 of type ι → ι → ι → ι → ι → ι → ι be given.
Apply H1 with
λ x4 : ι → ι → ι → ι → ι → ι → ι . (TwoRamseyGraph_4_6_Church6_squared_a x4 x1 x2 x3 = λ x5 x6 . x5) ⟶ TwoRamseyGraph_4_6_Church6_squared_a x2 x3 x4 x1 = λ x5 x6 . x5 leaving 6 subgoals.
Apply H2 with
λ x4 : ι → ι → ι → ι → ι → ι → ι . (TwoRamseyGraph_4_6_Church6_squared_a (λ x5 x6 x7 x8 x9 x10 . x5) x4 x2 x3 = λ x5 x6 . x5) ⟶ TwoRamseyGraph_4_6_Church6_squared_a x2 x3 (λ x5 x6 x7 x8 x9 x10 . x5) x4 = λ x5 x6 . x5 leaving 6 subgoals.
Apply H3 with
λ x4 : ι → ι → ι → ι → ι → ι → ι . (TwoRamseyGraph_4_6_Church6_squared_a (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x5) x4 x3 = λ x5 x6 . x5) ⟶ TwoRamseyGraph_4_6_Church6_squared_a x4 x3 (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x5) = λ x5 x6 . x5 leaving 6 subgoals.
Apply H4 with
λ x4 : ι → ι → ι → ι → ι → ι → ι . (TwoRamseyGraph_4_6_Church6_squared_a (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x5) x4 = λ x5 x6 . x5) ⟶ TwoRamseyGraph_4_6_Church6_squared_a (λ x5 x6 x7 x8 x9 x10 . x5) x4 (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x5) = λ x5 x6 . x5 leaving 6 subgoals.
Let x4 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H6:
x4 (TwoRamseyGraph_4_6_Church6_squared_a (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x5)) (λ x5 x6 . x5).
The subproof is completed by applying H6.
Apply FalseE with
TwoRamseyGraph_4_6_Church6_squared_a (λ x4 x5 x6 x7 x8 x9 . x4) (λ x4 x5 x6 x7 x8 x9 . x5) (λ x4 x5 x6 x7 x8 x9 . x4) (λ x4 x5 x6 x7 x8 x9 . x4) = λ x4 x5 . x4.
Apply L0.
The subproof is completed by applying H5.
Let x4 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H6:
x4 (TwoRamseyGraph_4_6_Church6_squared_a (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x7) (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x5)) (λ x5 x6 . x5).
The subproof is completed by applying H6.
Apply FalseE with
TwoRamseyGraph_4_6_Church6_squared_a (λ x4 x5 x6 x7 x8 x9 . x4) (λ x4 x5 x6 x7 x8 x9 . x7) (λ x4 x5 x6 x7 x8 x9 . x4) (λ x4 x5 x6 x7 x8 x9 . x4) = λ x4 x5 . x4.
Apply L0.
The subproof is completed by applying H5.
Let x4 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H6:
x4 (TwoRamseyGraph_4_6_Church6_squared_a (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x9) (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x5)) (λ x5 x6 . x5).
The subproof is completed by applying H6.
Apply FalseE with
TwoRamseyGraph_4_6_Church6_squared_a (λ x4 x5 x6 x7 x8 x9 . x4) (λ x4 x5 x6 x7 x8 x9 . x9) (λ x4 x5 x6 x7 x8 x9 . x4) (λ x4 x5 x6 x7 x8 x9 . x4) = λ x4 x5 . x4.
Apply L0.
The subproof is completed by applying H5.
Apply H4 with
λ x4 : ι → ι → ι → ι → ι → ι → ι . ... ⟶ TwoRamseyGraph_4_6_Church6_squared_a (λ x5 x6 x7 x8 x9 x10 . x6) x4 (λ x5 x6 x7 x8 x9 x10 . ...) ... = ... leaving 6 subgoals.