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Proofgold Proof

pf
Claim L0: ...
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Let x0 of type ιιιιιιι be given.
Let x1 of type ιιιιιιι be given.
Let x2 of type ιιιιιιι be given.
Let x3 of type ιιιιιιι be given.
Assume H1: Church6_p x0.
Assume H2: Church6_lt4p x1.
Assume H3: Church6_p x2.
Assume H4: Church6_lt4p x3.
Apply H1 with λ x4 : ι → ι → ι → ι → ι → ι → ι . (TwoRamseyGraph_4_6_Church6_squared_b x4 (permargs_i_1_0_3_2_4_5 x1) x2 (permargs_i_1_0_3_2_4_5 x3) = λ x5 x6 . x5)TwoRamseyGraph_4_6_Church6_squared_b x4 x1 x2 x3 = λ x5 x6 . x5 leaving 6 subgoals.
Apply H2 with λ x4 : ι → ι → ι → ι → ι → ι → ι . (TwoRamseyGraph_4_6_Church6_squared_b (λ x5 x6 x7 x8 x9 x10 . x5) (permargs_i_1_0_3_2_4_5 x4) x2 (permargs_i_1_0_3_2_4_5 x3) = λ x5 x6 . x5)TwoRamseyGraph_4_6_Church6_squared_b (λ x5 x6 x7 x8 x9 x10 . x5) x4 x2 x3 = λ x5 x6 . x5 leaving 4 subgoals.
Apply H3 with λ x4 : ι → ι → ι → ι → ι → ι → ι . (TwoRamseyGraph_4_6_Church6_squared_b (λ x5 x6 x7 x8 x9 x10 . x5) (permargs_i_1_0_3_2_4_5 (λ x5 x6 x7 x8 x9 x10 . x5)) x4 (permargs_i_1_0_3_2_4_5 x3) = λ x5 x6 . x5)TwoRamseyGraph_4_6_Church6_squared_b (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x5) x4 x3 = λ x5 x6 . x5 leaving 6 subgoals.
Apply H4 with λ x4 : ι → ι → ι → ι → ι → ι → ι . (TwoRamseyGraph_4_6_Church6_squared_b (λ x5 x6 x7 x8 x9 x10 . x5) (permargs_i_1_0_3_2_4_5 (λ x5 x6 x7 x8 x9 x10 . x5)) (λ x5 x6 x7 x8 x9 x10 . x5) (permargs_i_1_0_3_2_4_5 x4) = λ x5 x6 . x5)TwoRamseyGraph_4_6_Church6_squared_b (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 leaving 4 subgoals.
Assume H5: TwoRamseyGraph_4_6_Church6_squared_b (λ x4 x5 x6 x7 x8 x9 . x4) (permargs_i_1_0_3_2_4_5 (λ x4 x5 x6 x7 x8 x9 . x4)) (λ x4 x5 x6 x7 x8 x9 . x4) (permargs_i_1_0_3_2_4_5 (λ x4 x5 x6 x7 x8 x9 . x4)) = λ x4 x5 . x4.
Apply FalseE with TwoRamseyGraph_4_6_Church6_squared_b (λ x4 x5 x6 x7 x8 x9 . x4) (λ x4 x5 x6 x7 x8 x9 . x4) (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.
Assume H5: TwoRamseyGraph_4_6_Church6_squared_b (λ x4 x5 x6 x7 x8 x9 . x4) (permargs_i_1_0_3_2_4_5 (λ x4 x5 x6 x7 x8 x9 . x4)) (λ x4 x5 x6 x7 x8 x9 . x4) (permargs_i_1_0_3_2_4_5 (λ x4 x5 x6 x7 x8 x9 . x5)) = λ x4 x5 . x4.
Apply FalseE with TwoRamseyGraph_4_6_Church6_squared_b (λ x4 x5 x6 x7 x8 x9 . x4) (λ x4 x5 x6 x7 x8 x9 . x4) (λ x4 x5 x6 x7 x8 x9 . x4) (λ x4 x5 x6 x7 x8 x9 . x5) = λ x4 x5 . x4.
Apply L0.
The subproof is completed by applying H5.
Assume H5: TwoRamseyGraph_4_6_Church6_squared_b (λ x4 x5 x6 x7 x8 x9 . x4) (permargs_i_1_0_3_2_4_5 (λ x4 x5 x6 x7 x8 x9 . x4)) (λ x4 x5 x6 x7 x8 x9 . x4) (permargs_i_1_0_3_2_4_5 (λ x4 x5 x6 x7 x8 x9 . x6)) = λ x4 x5 . x4.
Let x4 of type (ιιι) → (ιιι) → ο be given.
Assume H6: x4 (TwoRamseyGraph_4_6_Church6_squared_b (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 . x7)) (λ x5 x6 . x5).
The subproof is completed by applying H6.
Assume H5: TwoRamseyGraph_4_6_Church6_squared_b (λ x4 x5 x6 x7 x8 x9 . x4) (permargs_i_1_0_3_2_4_5 (λ x4 x5 x6 x7 x8 x9 . x4)) (λ x4 x5 x6 x7 x8 x9 . x4) (permargs_i_1_0_3_2_4_5 (λ x4 x5 x6 x7 x8 x9 . x7)) = λ x4 x5 . x4.
Apply FalseE with TwoRamseyGraph_4_6_Church6_squared_b (λ x4 x5 x6 x7 x8 x9 . x4) (λ x4 x5 x6 x7 x8 x9 . x4) (λ x4 x5 x6 x7 x8 x9 . x4) (λ x4 x5 x6 x7 x8 x9 . x7) = 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_b (λ x5 x6 x7 x8 x9 x10 . x5) (permargs_i_1_0_3_2_4_5 (λ x5 x6 x7 x8 x9 x10 . x5)) (λ x5 x6 x7 x8 x9 x10 . x6) (permargs_i_1_0_3_2_4_5 x4) = λ x5 x6 . x5)TwoRamseyGraph_4_6_Church6_squared_b (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x6) x4 = λ x5 x6 . x5 leaving 4 subgoals.
Assume H5: TwoRamseyGraph_4_6_Church6_squared_b (λ x4 x5 x6 x7 x8 x9 . x4) (permargs_i_1_0_3_2_4_5 (λ x4 x5 x6 x7 x8 x9 . x4)) (λ x4 x5 x6 x7 x8 x9 . x5) (permargs_i_1_0_3_2_4_5 (λ x4 x5 x6 x7 x8 x9 . x4)) = λ x4 x5 . x4.
Let x4 of type (ιιι) → (ιιι) → ο be given.
Assume H6: x4 (TwoRamseyGraph_4_6_Church6_squared_b (λ x5 x6 x7 x8 x9 x10 . x5) (λ x5 x6 x7 x8 x9 x10 . x5) ... ...) ....
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