Proofgold Signed Transaction

Definition Church17_p := λ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . ∀ x1 : (ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι) → ο . x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x2) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x3) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x4) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x5) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x6) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x7) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x8) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x9) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x10) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x11) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x12) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x13) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x14) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x15) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x16) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x17) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x18) ⟶ x1 x0
Definition TwoRamseyGraph_3_6_Church17 := λ x0 x1 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . λ x2 x3 . x0 (x1 x2 x2 x2 x3 x3 x3 x3 x2 x3 x3 x2 x3 x3 x3 x3 x2 x3) (x1 x2 x2 x3 x2 x3 x3 x2 x3 x3 x3 x3 x2 x2 x3 x3 x3 x3) (x1 x2 x3 x2 x2 x3 x2 x3 x3 x2 x3 x3 x3 x3 x3 x2 x3 x3) (x1 x3 x2 x2 x2 x2 x3 x3 x3 x3 x2 x3 x3 x3 x2 x3 x3 x3) (x1 x3 x3 x3 x2 x2 x2 x2 x3 x3 x3 x2 x3 x3 x3 x3 x2 x3) (x1 x3 x3 x2 x3 x2 x2 x3 x2 x3 x3 x3 x2 x2 x3 x3 x3 x3) (x1 x3 x2 x3 x3 x2 x3 x2 x2 x2 x3 x3 x3 x3 x3 x2 x3 x3) (x1 x2 x3 x3 x3 x3 x2 x2 x2 x3 x2 x3 x3 x3 x2 x3 x3 x3) (x1 x3 x3 x2 x3 x3 x3 x2 x3 x2 x3 x3 x2 x2 x2 x3 x3 x3) (x1 x3 x3 x3 x2 x3 x3 x3 x2 x3 x2 x2 x3 x2 x3 x3 x2 x3) (x1 x2 x3 x3 x3 x2 x3 x3 x3 x3 x2 x2 x3 x3 x2 x2 x3 x3) (x1 x3 x2 x3 x3 x3 x2 x3 x3 x2 x3 x3 x2 x3 x3 x2 x2 x3) (x1 x3 x2 x3 x3 x3 x2 x3 x3 x2 x2 x3 x3 x2 x3 x3 x3 x2) (x1 x3 x3 x3 x2 x3 x3 x3 x2 x2 x3 x2 x3 x3 x2 x3 x3 x2) (x1 x3 x3 x2 x3 x3 x3 x2 x3 x3 x3 x2 x2 x3 x3 x2 x3 x2) (x1 x2 x3 x3 x3 x2 x3 x3 x3 x3 x2 x3 x2 x3 x3 x3 x2 x2) (x1 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x2 x2 x2 x2 x2)
Theorem 65c75.. : ∀ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_p x0 ⟶ TwoRamseyGraph_3_6_Church17 x0 x0 = λ x2 x3 . x2 (proof)
Param ordsucc^ordsucc : ι → ι
Definition u1 := 1
Definition u2 := ordsucc u1
Definition u3 := ordsucc u2
Definition u4 := ordsucc u3
Definition u5 := ordsucc u4
Definition u6 := ordsucc u5
Definition u7 := ordsucc u6
Definition u8 := ordsucc u7
Definition u9 := ordsucc u8
Definition u10 := ordsucc u9
Definition u11 := ordsucc u10
Definition u12 := ordsucc u11
Definition u13 := ordsucc u12
Definition u14 := ordsucc u13
Definition u15 := ordsucc u14
Definition u16 := ordsucc u15
Definition u17 := ordsucc u16
Param u17_to_Church17 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι
Definition TwoRamseyGraph_3_6_17 := λ x0 x1 . x0 ∈ u17 ⟶ x1 ∈ u17 ⟶ TwoRamseyGraph_3_6_Church17 (u17_to_Church17 x0) (u17_to_Church17 x1) = λ x3 x4 . x3
Param u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 : ι → ι
Known 660da.. : ∀ x0 . x0 ∈ u16 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 u1 ⟶ x1 u2 ⟶ x1 u3 ⟶ x1 u4 ⟶ x1 u5 ⟶ x1 u6 ⟶ x1 u7 ⟶ x1 u8 ⟶ x1 u9 ⟶ x1 u10 ⟶ x1 u11 ⟶ x1 u12 ⟶ x1 u13 ⟶ x1 u14 ⟶ x1 u15 ⟶ x1 x0
Definition False^False := ∀ x0 : ο . x0
Known FalseE^FalseE : False ⟶ ∀ x0 : ο . x0
Definition not^not := λ x0 : ο . x0 ⟶ False
Definition nIn^nIn := λ x0 x1 . not (x0 ∈ x1)
Known EmptyE^EmptyE : ∀ x0 . nIn x0 0
Known cases_1^cases_1 : ∀ x0 . x0 ∈ 1 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 x0
Known b0ce1.. : u17_to_Church17 u1 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x2
Known c5926.. : u17_to_Church17 0 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x1
Known cases_2^cases_2 : ∀ x0 . x0 ∈ 2 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 1 ⟶ x1 x0
Known e8ec5.. : u17_to_Church17 u2 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x3
Known 00076.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u2 = 0
Known 6eb3e.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u1 = u3
Known 1ef08.. : u17_to_Church17 u3 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x4
Known c5b55.. : 0 ∈ u17
Known 35c0a.. : u3 ∈ u17
Known cases_3^cases_3 : ∀ x0 . x0 ∈ 3 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 1 ⟶ x1 2 ⟶ x1 x0
Known 737c8.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u3 = u2
Known 428fd.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 0 = u1
Known 9502b.. : u2 ∈ u17
Known f6e42.. : u1 ∈ u17
Known cases_4^cases_4 : ∀ x0 . x0 ∈ 4 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 1 ⟶ x1 2 ⟶ x1 3 ⟶ x1 x0
Known b5b60.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u4 = u5
Known 22977.. : u17_to_Church17 u5 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x6
Known 79c48.. : u5 ∈ u17
Known 05513.. : u17_to_Church17 u4 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x5
Known cases_5^cases_5 : ∀ x0 . x0 ∈ 5 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 1 ⟶ x1 2 ⟶ x1 3 ⟶ x1 4 ⟶ x1 x0
Known d3a23.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u5 = u7
Known b0f83.. : u17_to_Church17 u7 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x8
Known 51ef0.. : u7 ∈ u17
Known cases_6^cases_6 : ∀ x0 . x0 ∈ 6 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 1 ⟶ x1 2 ⟶ x1 3 ⟶ x1 4 ⟶ x1 5 ⟶ x1 x0
Known 9e037.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u6 = u4
Known 793dd.. : u4 ∈ u17
Known 0e32a.. : u17_to_Church17 u6 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x7
Known cases_7^cases_7 : ∀ x0 . x0 ∈ 7 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 1 ⟶ x1 2 ⟶ x1 3 ⟶ x1 4 ⟶ x1 5 ⟶ x1 6 ⟶ x1 x0
Known af667.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u7 = u6
Known b3205.. : u6 ∈ u17
Known cases_8^cases_8 : ∀ x0 . x0 ∈ 8 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 1 ⟶ x1 2 ⟶ x1 3 ⟶ x1 4 ⟶ x1 5 ⟶ x1 6 ⟶ x1 7 ⟶ x1 x0
Known 86df1.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u8 = u10
Known d7087.. : u17_to_Church17 u10 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x11
Known e886d.. : u10 ∈ u17
Known 48ba7.. : u17_to_Church17 u8 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x9
Known cases_9^cases_9 : ∀ x0 . x0 ∈ 9 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 1 ⟶ x1 2 ⟶ x1 3 ⟶ x1 4 ⟶ x1 5 ⟶ x1 6 ⟶ x1 7 ⟶ x1 8 ⟶ x1 x0
Known 1f384.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u9 = u8
Known 6a4e9.. : u8 ∈ u17
Known a3fb1.. : u17_to_Church17 u9 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x10
Known 44418.. : ∀ x0 . x0 ∈ u10 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 u1 ⟶ x1 u2 ⟶ x1 u3 ⟶ x1 u4 ⟶ x1 u5 ⟶ x1 u6 ⟶ x1 u7 ⟶ x1 u8 ⟶ x1 u9 ⟶ x1 x0
Known f964e.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u10 = u11
Known a87a3.. : u17_to_Church17 u11 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x12
Known e57ea.. : u11 ∈ u17
Known 83484.. : ∀ x0 . x0 ∈ u11 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 u1 ⟶ x1 u2 ⟶ x1 u3 ⟶ x1 u4 ⟶ x1 u5 ⟶ x1 u6 ⟶ x1 u7 ⟶ x1 u8 ⟶ x1 u9 ⟶ x1 u10 ⟶ x1 x0
Known 1f07b.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u11 = u9
Known fd1a6.. : u9 ∈ u17
Known 866c8.. : ∀ x0 . x0 ∈ u12 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 u1 ⟶ x1 u2 ⟶ x1 u3 ⟶ x1 u4 ⟶ x1 u5 ⟶ x1 u6 ⟶ x1 u7 ⟶ x1 u8 ⟶ x1 u9 ⟶ x1 u10 ⟶ x1 u11 ⟶ x1 x0
Known be3a6.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u12 = u13
Known 0975c.. : u17_to_Church17 u13 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x14
Known 7315d.. : u13 ∈ u17
Known a52d8.. : u17_to_Church17 u12 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x13
Known 6de8d.. : ∀ x0 . x0 ∈ u13 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 u1 ⟶ x1 u2 ⟶ x1 u3 ⟶ x1 u4 ⟶ x1 u5 ⟶ x1 u6 ⟶ x1 u7 ⟶ x1 u8 ⟶ x1 u9 ⟶ x1 u10 ⟶ x1 u11 ⟶ x1 u12 ⟶ x1 x0
Known 0e84a.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u13 = u14
Known cf897.. : u17_to_Church17 u14 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x15
Known 35e01.. : u14 ∈ u17
Known dca77.. : ∀ x0 . x0 ∈ u14 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 u1 ⟶ x1 u2 ⟶ x1 u3 ⟶ x1 u4 ⟶ x1 u5 ⟶ x1 u6 ⟶ x1 u7 ⟶ x1 u8 ⟶ x1 u9 ⟶ x1 u10 ⟶ x1 u11 ⟶ x1 u12 ⟶ x1 u13 ⟶ x1 x0
Known 4b6e2.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u14 = u15
Known c424d.. : u17_to_Church17 u15 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x16
Known 31b8d.. : u15 ∈ u17
Known f3498.. : ∀ x0 . x0 ∈ u15 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 u1 ⟶ x1 u2 ⟶ x1 u3 ⟶ x1 u4 ⟶ x1 u5 ⟶ x1 u6 ⟶ x1 u7 ⟶ x1 u8 ⟶ x1 u9 ⟶ x1 u10 ⟶ x1 u11 ⟶ x1 u12 ⟶ x1 u13 ⟶ x1 u14 ⟶ x1 x0
Known 5681c.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u15 = u12
Known a1a10.. : u12 ∈ u17
Known 768c1.. : ((λ x1 x2 . x2) = λ x1 x2 . x1) ⟶ ∀ x0 : ο . x0
Theorem 50c64.. : ∀ x0 . x0 ∈ u16 ⟶ ∀ x1 . x1 ∈ x0 ⟶ TwoRamseyGraph_3_6_17 (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0) (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x1) ⟶ TwoRamseyGraph_3_6_17 x0 x1 (proof)
Param ordinal^ordinal : ι → ο
Known ordinal_trichotomy_or_impred^{ordinal_trichotomy_or_impred} : ∀ x0 x1 . ordinal x0 ⟶ ordinal x1 ⟶ ∀ x2 : ο . (x0 ∈ x1 ⟶ x2) ⟶ (x0 = x1 ⟶ x2) ⟶ (x1 ∈ x0 ⟶ x2) ⟶ x2
Param nat_p^nat_p : ι → ο
Known nat_p_ordinal^{nat_p_ordinal} : ∀ x0 . nat_p x0 ⟶ ordinal x0
Known nat_p_trans^nat_p_trans : ∀ x0 . nat_p x0 ⟶ ∀ x1 . x1 ∈ x0 ⟶ nat_p x1
Known nat_16^nat_16 : nat_p 16
Known 72dc0.. : ∀ x0 x1 . TwoRamseyGraph_3_6_17 x0 x1 ⟶ TwoRamseyGraph_3_6_17 x1 x0
Known db165.. : ∀ x0 . x0 ∈ u17 ⟶ Church17_p (u17_to_Church17 x0)
Definition Subq^Subq := λ x0 x1 . ∀ x2 . x2 ∈ x0 ⟶ x2 ∈ x1
Known ordsuccI1^ordsuccI1 : ∀ x0 . x0 ⊆ ordsucc x0
Theorem 36aae.. : ∀ x0 . x0 ∈ u16 ⟶ ∀ x1 . x1 ∈ u16 ⟶ TwoRamseyGraph_3_6_17 (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0) (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x1) ⟶ TwoRamseyGraph_3_6_17 x0 x1 (proof)
Known neq_3_1^neq_3_1 : u3 = u1 ⟶ ∀ x0 : ο . x0
Known neq_1_0^neq_1_0 : u1 = 0 ⟶ ∀ x0 : ο . x0
Known neq_3_0^neq_3_0 : u3 = 0 ⟶ ∀ x0 : ο . x0
Known neq_2_1^neq_2_1 : u2 = u1 ⟶ ∀ x0 : ο . x0
Known neq_3_2^neq_3_2 : u3 = u2 ⟶ ∀ x0 : ο . x0
Known neq_2_0^neq_2_0 : u2 = 0 ⟶ ∀ x0 : ο . x0
Known neq_5_1^neq_5_1 : u5 = u1 ⟶ ∀ x0 : ο . x0
Known neq_5_3^neq_5_3 : u5 = u3 ⟶ ∀ x0 : ο . x0
Known neq_5_0^neq_5_0 : u5 = 0 ⟶ ∀ x0 : ο . x0
Known neq_5_2^neq_5_2 : u5 = u2 ⟶ ∀ x0 : ο . x0
Known neq_7_1^neq_7_1 : u7 = u1 ⟶ ∀ x0 : ο . x0
Known neq_7_3^neq_7_3 : u7 = u3 ⟶ ∀ x0 : ο . x0
Known neq_7_0^neq_7_0 : u7 = 0 ⟶ ∀ x0 : ο . x0
Known neq_7_2^neq_7_2 : u7 = u2 ⟶ ∀ x0 : ο . x0
Known neq_7_5^neq_7_5 : u7 = u5 ⟶ ∀ x0 : ο . x0
Known neq_4_1^neq_4_1 : u4 = u1 ⟶ ∀ x0 : ο . x0
Known neq_4_3^neq_4_3 : u4 = u3 ⟶ ∀ x0 : ο . x0
Known neq_4_0^neq_4_0 : u4 = 0 ⟶ ∀ x0 : ο . x0
Known neq_4_2^neq_4_2 : u4 = u2 ⟶ ∀ x0 : ο . x0
Known neq_5_4^neq_5_4 : u5 = u4 ⟶ ∀ x0 : ο . x0
Known neq_7_4^neq_7_4 : u7 = u4 ⟶ ∀ x0 : ο . x0
Known neq_6_1^neq_6_1 : u6 = u1 ⟶ ∀ x0 : ο . x0
Known neq_6_3^neq_6_3 : u6 = u3 ⟶ ∀ x0 : ο . x0
Known neq_6_0^neq_6_0 : u6 = 0 ⟶ ∀ x0 : ο . x0
Known neq_6_2^neq_6_2 : u6 = u2 ⟶ ∀ x0 : ο . x0
Known neq_6_5^neq_6_5 : u6 = u5 ⟶ ∀ x0 : ο . x0
Known neq_7_6^neq_7_6 : u7 = u6 ⟶ ∀ x0 : ο . x0
Known neq_6_4^neq_6_4 : u6 = u4 ⟶ ∀ x0 : ο . x0
Known d183f.. : u10 = u1 ⟶ ∀ x0 : ο . x0
Known 68152.. : u10 = u3 ⟶ ∀ x0 : ο . x0
Known 0e10e.. : u10 = 0 ⟶ ∀ x0 : ο . x0
Known e02d9.. : u10 = u2 ⟶ ∀ x0 : ο . x0
Known a7d50.. : u10 = u5 ⟶ ∀ x0 : ο . x0
Known 7d7a8.. : u10 = u7 ⟶ ∀ x0 : ο . x0
Known 33d16.. : u10 = u4 ⟶ ∀ x0 : ο . x0
Known d0401.. : u10 = u6 ⟶ ∀ x0 : ο . x0
Known neq_8_1^neq_8_1 : u8 = u1 ⟶ ∀ x0 : ο . x0
Known neq_8_3^neq_8_3 : u8 = u3 ⟶ ∀ x0 : ο . x0
Known neq_8_0^neq_8_0 : u8 = 0 ⟶ ∀ x0 : ο . x0
Known neq_8_2^neq_8_2 : u8 = u2 ⟶ ∀ x0 : ο . x0
Known neq_8_5^neq_8_5 : u8 = u5 ⟶ ∀ x0 : ο . x0
Known neq_8_7^neq_8_7 : u8 = u7 ⟶ ∀ x0 : ο . x0
Known neq_8_4^neq_8_4 : u8 = u4 ⟶ ∀ x0 : ο . x0
Known neq_8_6^neq_8_6 : u8 = u6 ⟶ ∀ x0 : ο . x0
Known 96175.. : u10 = u8 ⟶ ∀ x0 : ο . x0
Known 618f7.. : u11 = u1 ⟶ ∀ x0 : ο . x0
Known b06e1.. : u11 = u3 ⟶ ∀ x0 : ο . x0
Known 19f75.. : u11 = 0 ⟶ ∀ x0 : ο . x0
Known 2c42c.. : u11 = u2 ⟶ ∀ x0 : ο . x0
Known 1b659.. : u11 = u5 ⟶ ∀ x0 : ο . x0
Known 4abfa.. : u11 = u7 ⟶ ∀ x0 : ο . x0
Known 6a6f1.. : u11 = u4 ⟶ ∀ x0 : ο . x0
Known 949f2.. : u11 = u6 ⟶ ∀ x0 : ο . x0
Known ebfb7.. : u11 = u10 ⟶ ∀ x0 : ο . x0
Known b3a20.. : u11 = u8 ⟶ ∀ x0 : ο . x0
Known neq_9_1^neq_9_1 : u9 = u1 ⟶ ∀ x0 : ο . x0
Known neq_9_3^neq_9_3 : u9 = u3 ⟶ ∀ x0 : ο . x0
Known neq_9_0^neq_9_0 : u9 = 0 ⟶ ∀ x0 : ο . x0
Known neq_9_2^neq_9_2 : u9 = u2 ⟶ ∀ x0 : ο . x0
Known neq_9_5^neq_9_5 : u9 = u5 ⟶ ∀ x0 : ο . x0
Known neq_9_7^neq_9_7 : u9 = u7 ⟶ ∀ x0 : ο . x0
Known neq_9_4^neq_9_4 : u9 = u4 ⟶ ∀ x0 : ο . x0
Known neq_9_6^neq_9_6 : u9 = u6 ⟶ ∀ x0 : ο . x0
Known 4fc31.. : u10 = u9 ⟶ ∀ x0 : ο . x0
Known neq_9_8^neq_9_8 : u9 = u8 ⟶ ∀ x0 : ο . x0
Known 4f03f.. : u11 = u9 ⟶ ∀ x0 : ο . x0
Known 16246.. : u13 = u1 ⟶ ∀ x0 : ο . x0
Known 19222.. : u13 = u3 ⟶ ∀ x0 : ο . x0
Known 733b2.. : u13 = 0 ⟶ ∀ x0 : ο . x0
Known 40d25.. : u13 = u2 ⟶ ∀ x0 : ο . x0
Known 29333.. : u13 = u5 ⟶ ∀ x0 : ο . x0
Known d9b35.. : u13 = u7 ⟶ ∀ x0 : ο . x0
Known 4d850.. : u13 = u4 ⟶ ∀ x0 : ο . x0
Known 02f5c.. : u13 = u6 ⟶ ∀ x0 : ο . x0
Known 78358.. : u13 = u10 ⟶ ∀ x0 : ο . x0
Known 0b225.. : u13 = u8 ⟶ ∀ x0 : ο . x0
Known bf497.. : u13 = u11 ⟶ ∀ x0 : ο . x0
Known 3f24c.. : u13 = u9 ⟶ ∀ x0 : ο . x0
Known ac679.. : u14 = u1 ⟶ ∀ x0 : ο . x0
Known d0fe4.. : u14 = u3 ⟶ ∀ x0 : ο . x0
Known fc551.. : u14 = 0 ⟶ ∀ x0 : ο . x0
Known 0bb18.. : u14 = u2 ⟶ ∀ x0 : ο . x0
Known d6c57.. : u14 = u5 ⟶ ∀ x0 : ο . x0
Known 01bf6.. : u14 = u7 ⟶ ∀ x0 : ο . x0
Known ffd62.. : u14 = u4 ⟶ ∀ x0 : ο . x0
Known 62d80.. : u14 = u6 ⟶ ∀ x0 : ο . x0
Known f5ab5.. : u14 = u10 ⟶ ∀ x0 : ο . x0
Known 4f6ad.. : u14 = u8 ⟶ ∀ x0 : ο . x0
Known 4e1aa.. : u14 = u11 ⟶ ∀ x0 : ο . x0
Known d7730.. : u14 = u9 ⟶ ∀ x0 : ο . x0
Known e1947.. : u14 = u13 ⟶ ∀ x0 : ο . x0
Known 174d1.. : u15 = u1 ⟶ ∀ x0 : ο . x0
Known 70124.. : u15 = u3 ⟶ ∀ x0 : ο . x0
Known 160ad.. : u15 = 0 ⟶ ∀ x0 : ο . x0
Known 4d715.. : u15 = u2 ⟶ ∀ x0 : ο . x0
Known 24fad.. : u15 = u5 ⟶ ∀ x0 : ο . x0
Known 008b1.. : u15 = u7 ⟶ ∀ x0 : ο . x0
Known 4b742.. : u15 = u4 ⟶ ∀ x0 : ο . x0
Known f5ac7.. : u15 = u6 ⟶ ∀ x0 : ο . x0
Known b7f53.. : u15 = u10 ⟶ ∀ x0 : ο . x0
Known c0d75.. : u15 = u8 ⟶ ∀ x0 : ο . x0
Known 9c5db.. : u15 = u11 ⟶ ∀ x0 : ο . x0
Known 3a7bc.. : u15 = u9 ⟶ ∀ x0 : ο . x0
Known 4d8d4.. : u15 = u13 ⟶ ∀ x0 : ο . x0
Known b8e82.. : u15 = u14 ⟶ ∀ x0 : ο . x0
Known ce0cd.. : u12 = u1 ⟶ ∀ x0 : ο . x0
Known e015c.. : u12 = u3 ⟶ ∀ x0 : ο . x0
Known efdfc.. : u12 = 0 ⟶ ∀ x0 : ο . x0
Known 8158b.. : u12 = u2 ⟶ ∀ x0 : ο . x0
Known 07eba.. : u12 = u5 ⟶ ∀ x0 : ο . x0
Known 6a15f.. : u12 = u7 ⟶ ∀ x0 : ο . x0
Known 7aa79.. : u12 = u4 ⟶ ∀ x0 : ο . x0
Known 0bd83.. : u12 = u6 ⟶ ∀ x0 : ο . x0
Known 6c583.. : u12 = u10 ⟶ ∀ x0 : ο . x0
Known a6a6c.. : u12 = u8 ⟶ ∀ x0 : ο . x0
Known ab306.. : u12 = u11 ⟶ ∀ x0 : ο . x0
Known 22885.. : u12 = u9 ⟶ ∀ x0 : ο . x0
Known ad02f.. : u13 = u12 ⟶ ∀ x0 : ο . x0
Known ef4da.. : u14 = u12 ⟶ ∀ x0 : ο . x0
Known 72647.. : u15 = u12 ⟶ ∀ x0 : ο . x0
Theorem ef8a4.. : ∀ x0 . x0 ∈ u16 ⟶ ∀ x1 . x1 ∈ x0 ⟶ u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0 = u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x1 ⟶ ∀ x2 : ο . x2 (proof)
Theorem f2c34.. : ∀ x0 . x0 ∈ u16 ⟶ ∀ x1 . x1 ∈ u16 ⟶ u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0 = u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x1 ⟶ x0 = x1 (proof)
Theorem 01145.. : ∀ x0 . x0 ∈ u16 ⟶ u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0))) = x0 (proof)