Search for blocks/addresses/...

Proofgold Address

address
PUWEWBE6byXMcaPfRLCqc1ZABr1FrJMfB1q
total
0
mg
-
conjpub
-
current assets
8efa8../197f4.. bday: 35824 doc published by Pr4zB..
Param 4402e.. : ι(ιιο) → ο
Param cf2df.. : ι(ιιο) → ο
Definition SubqSubq := λ x0 x1 . ∀ x2 . x2x0x2x1
Param setminussetminus : ιιι
Param SingSing : ιι
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Definition 8b6ad.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 . ∀ x5 : ο . ((x1 = x2∀ x6 : ο . x6)(x1 = x3∀ x6 : ο . x6)(x2 = x3∀ x6 : ο . x6)(x1 = x4∀ x6 : ο . x6)(x2 = x4∀ x6 : ο . x6)(x3 = x4∀ x6 : ο . x6)not (x0 x1 x2)not (x0 x1 x3)not (x0 x2 x3)not (x0 x1 x4)not (x0 x2 x4)not (x0 x3 x4)x5)x5
Definition c5756.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 . ∀ x6 : ο . (8b6ad.. x0 x1 x2 x3 x4(x1 = x5∀ x7 : ο . x7)(x2 = x5∀ x7 : ο . x7)(x3 = x5∀ x7 : ο . x7)(x4 = x5∀ x7 : ο . x7)not (x0 x1 x5)not (x0 x2 x5)x0 x3 x5x0 x4 x5x6)x6
Definition ba720.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (c5756.. x0 x1 x2 x3 x4 x5(x1 = x6∀ x8 : ο . x8)(x2 = x6∀ x8 : ο . x8)(x3 = x6∀ x8 : ο . x8)(x4 = x6∀ x8 : ο . x8)(x5 = x6∀ x8 : ο . x8)x0 x1 x6x0 x2 x6not (x0 x3 x6)x0 x4 x6not (x0 x5 x6)x7)x7
Definition 28532.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (ba720.. x0 x1 x2 x3 x4 x5 x6(x1 = x7∀ x9 : ο . x9)(x2 = x7∀ x9 : ο . x9)(x3 = x7∀ x9 : ο . x9)(x4 = x7∀ x9 : ο . x9)(x5 = x7∀ x9 : ο . x9)(x6 = x7∀ x9 : ο . x9)x0 x1 x7x0 x2 x7x0 x3 x7x0 x4 x7not (x0 x5 x7)not (x0 x6 x7)x8)x8
Definition e7651.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (28532.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)not (x0 x1 x8)not (x0 x2 x8)x0 x3 x8x0 x4 x8not (x0 x5 x8)not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition 2bd9d.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (28532.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)not (x0 x1 x8)x0 x2 x8not (x0 x3 x8)not (x0 x4 x8)not (x0 x5 x8)not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition 30182.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (2bd9d.. x0 x1 x2 x3 x4 x5 x6 x7 x8(x1 = x9∀ x11 : ο . x11)(x2 = x9∀ x11 : ο . x11)(x3 = x9∀ x11 : ο . x11)(x4 = x9∀ x11 : ο . x11)(x5 = x9∀ x11 : ο . x11)(x6 = x9∀ x11 : ο . x11)(x7 = x9∀ x11 : ο . x11)(x8 = x9∀ x11 : ο . x11)not (x0 x1 x9)not (x0 x2 x9)x0 x3 x9x0 x4 x9not (x0 x5 x9)not (x0 x6 x9)not (x0 x7 x9)x0 x8 x9x10)x10
Definition db72f.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (28532.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)x0 x1 x8x0 x2 x8not (x0 x3 x8)not (x0 x4 x8)not (x0 x5 x8)not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition 803e1.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (db72f.. x0 x1 x2 x3 x4 x5 x6 x7 x8(x1 = x9∀ x11 : ο . x11)(x2 = x9∀ x11 : ο . x11)(x3 = x9∀ x11 : ο . x11)(x4 = x9∀ x11 : ο . x11)(x5 = x9∀ x11 : ο . x11)(x6 = x9∀ x11 : ο . x11)(x7 = x9∀ x11 : ο . x11)(x8 = x9∀ x11 : ο . x11)not (x0 x1 x9)not (x0 x2 x9)x0 x3 x9x0 x4 x9not (x0 x5 x9)not (x0 x6 x9)not (x0 x7 x9)x0 x8 x9x10)x10
Definition d2a2c.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (e7651.. x0 x1 x2 x3 x4 x5 x6 x7 x8(x1 = x9∀ x11 : ο . x11)(x2 = x9∀ x11 : ο . x11)(x3 = x9∀ x11 : ο . x11)(x4 = x9∀ x11 : ο . x11)(x5 = x9∀ x11 : ο . x11)(x6 = x9∀ x11 : ο . x11)(x7 = x9∀ x11 : ο . x11)(x8 = x9∀ x11 : ο . x11)x0 x1 x9x0 x2 x9not (x0 x3 x9)not (x0 x4 x9)x0 x5 x9not (x0 x6 x9)not (x0 x7 x9)x0 x8 x9x10)x10
Definition andand := λ x0 x1 : ο . ∀ x2 : ο . (x0x1x2)x2
Definition nInnIn := λ x0 x1 . not (x0x1)
Known setminusEsetminusE : ∀ x0 x1 x2 . x2setminus x0 x1and (x2x0) (nIn x2 x1)
Known ad693.. : ∀ x0 x1 . ∀ x2 : ι → ι → ο . (∀ x3 . x3x1∀ x4 . x4x1x2 x3 x4x2 x4 x3)4402e.. x1 x2cf2df.. x1 x2∀ x3 . x3x1x0setminus x1 (Sing x3)∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0∀ x8 . x8x0∀ x9 . x9x0∀ x10 . x10x0∀ x11 . x11x0e7651.. x2 x4 x5 x6 x7 x8 x9 x10 x11∀ x12 : ο . (x2 x4 x3not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)not (x2 x11 x3)x12)(not (x2 x4 x3)x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)not (x2 x11 x3)x12)(x2 x4 x3x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)not (x2 x11 x3)x12)(x2 x4 x3not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x2 x11 x3x12)(not (x2 x4 x3)x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x2 x11 x3x12)(x2 x4 x3x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x2 x11 x3x12)(x2 x4 x3not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)x2 x11 x3x12)(not (x2 x4 x3)x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)x2 x11 x3x12)(x2 x4 x3x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)x2 x11 x3x12)x12
Known d7596.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x08b6ad.. x1 x2 x3 x4 x58b6ad.. x1 x3 x2 x4 x5
Known neq_i_symneq_i_sym : ∀ x0 x1 . (x0 = x1∀ x2 : ο . x2)x1 = x0∀ x2 : ο . x2
Known ff8ba.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0∀ x8 . x8x028532.. x1 x2 x3 x4 x5 x6 x7 x828532.. x1 x3 x2 x4 x5 x6 x7 x8
Known c255c.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0∀ x8 . x8x0∀ x9 . x9x0e7651.. x1 x2 x3 x4 x5 x6 x7 x8 x9e7651.. x1 x9 x6 x7 x8 x3 x4 x5 x2
Known Subq_traSubq_tra : ∀ x0 x1 x2 . x0x1x1x2x0x2
Known setminus_Subqsetminus_Subq : ∀ x0 x1 . setminus x0 x1x0
Known SingISingI : ∀ x0 . x0Sing x0
Theorem 8d708.. : ∀ x0 x1 . ∀ x2 : ι → ι → ο . (∀ x3 . x3x1∀ x4 . x4x1x2 x3 x4x2 x4 x3)4402e.. x1 x2cf2df.. x1 x2∀ x3 . x3x1x0setminus x1 (Sing x3)∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0∀ x8 . x8x0∀ x9 . x9x0∀ x10 . x10x0∀ x11 . x11x0e7651.. x2 x4 x5 x6 x7 x8 x9 x10 x11∀ x12 : ο . (∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0∀ x19 . x19x0∀ x20 . x20x030182.. x2 x13 x14 x15 x16 x17 x18 x19 x3 x20x12)(∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0∀ x19 . x19x0∀ x20 . x20x0803e1.. x2 x13 x14 x15 x16 x17 x18 x19 x3 x20x12)(∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0∀ x19 . x19x0∀ x20 . x20x0d2a2c.. x2 x13 x14 x15 x16 x17 x18 x19 x20 x3x12)x12 (proof)

previous assets