Let x0 of type ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι be given.
Let x1 of type ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι be given.
Let x2 of type ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι be given.
Apply H0 with
λ x3 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . (TwoRamseyGraph_3_6_Church17 x3 x1 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x3 x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x1 x2 = λ x4 x5 . x5) ⟶ ∀ x4 : ο . (84660.. x3 ⟶ x4) ⟶ (84660.. x1 ⟶ x4) ⟶ (84660.. x2 ⟶ x4) ⟶ x4 leaving 8 subgoals.
Apply H1 with
λ x3 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) x3 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x3 x2 = λ x4 x5 . x5) ⟶ ∀ x4 : ο . (84660.. (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x5) ⟶ x4) ⟶ (84660.. x3 ⟶ x4) ⟶ (84660.. x2 ⟶ x4) ⟶ x4 leaving 8 subgoals.
Assume H3:
TwoRamseyGraph_3_6_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) = λ x3 x4 . x4.
Apply FalseE with
(TwoRamseyGraph_3_6_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) x2 = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) x2 = λ x3 x4 . x4) ⟶ ∀ x3 : ο . (84660.. (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) ⟶ x3) ⟶ (84660.. (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) ⟶ x3) ⟶ (84660.. x2 ⟶ x3) ⟶ x3.
Apply unknownprop_1019f796b5519c5beeeef55b1daae2de48848a97e75d217687db0a2449fd5208.
Let x3 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
The subproof is completed by applying H3 with λ x4 x5 : ι → ι → ι . x3 x5 x4.
Assume H3:
TwoRamseyGraph_3_6_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x4) = λ x3 x4 . x4.
Apply FalseE with
(TwoRamseyGraph_3_6_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) x2 = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x4) x2 = λ x3 x4 . x4) ⟶ ∀ x3 : ο . (84660.. (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) ⟶ x3) ⟶ (84660.. (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x5) ⟶ x3) ⟶ (84660.. x2 ⟶ x3) ⟶ x3.
Apply unknownprop_1019f796b5519c5beeeef55b1daae2de48848a97e75d217687db0a2449fd5208.
Let x3 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
The subproof is completed by applying H3 with λ x4 x5 : ι → ι → ι . x3 x5 x4.
Assume H3:
TwoRamseyGraph_3_6_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x5) = λ x3 x4 . x4.
Apply FalseE with
(TwoRamseyGraph_3_6_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) x2 = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x5) x2 = λ x3 x4 . x4) ⟶ ∀ x3 : ο . (84660.. (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) ⟶ x3) ⟶ (84660.. (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x6) ⟶ x3) ⟶ (84660.. x2 ⟶ x3) ⟶ x3.
Apply unknownprop_1019f796b5519c5beeeef55b1daae2de48848a97e75d217687db0a2449fd5208.
Let x3 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
The subproof is completed by applying H3 with λ x4 x5 : ι → ι → ι . x3 x5 x4.
Apply H2 with
λ x3 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x7) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) x3 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x7) x3 = λ x4 x5 . x5) ⟶ ∀ x4 : ο . (84660.. (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x5) ⟶ x4) ⟶ (84660.. (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x8) ⟶ x4) ⟶ (84660.. x3 ⟶ x4) ⟶ x4 leaving 8 subgoals.
Assume H3:
TwoRamseyGraph_3_6_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x6) = λ x3 x4 . x4.
Assume H4:
TwoRamseyGraph_3_6_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) = λ x3 x4 . x4.
Apply FalseE with
... ⟶ ∀ x3 : ο . (... ⟶ x3) ⟶ (84660.. (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x7) ⟶ x3) ⟶ (84660.. (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) ⟶ x3) ⟶ x3.