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Proofgold Asset

asset id
b79274ccbaadfd8ad6ab0c5e3eab4073d21d86926a890272421bee90735b0602
asset hash
0ce192f53de6abb0cc7d184157d7ea2d4fbcc501c45660717fafb558bdd4b352
bday / block
36190
tx
bda39..
preasset
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 2de86.. := 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)not (x0 x1 x6)x0 x2 x6not (x0 x3 x6)x0 x4 x6not (x0 x5 x6)x7)x7
Definition 36d58.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (2de86.. 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 x7not (x0 x2 x7)x0 x3 x7x0 x4 x7not (x0 x5 x7)not (x0 x6 x7)x8)x8
Definition af16d.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (36d58.. 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)not (x0 x3 x8)x0 x4 x8not (x0 x5 x8)not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition a3794.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (af16d.. 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 x9not (x0 x2 x9)x0 x3 x9not (x0 x4 x9)not (x0 x5 x9)x0 x6 x9not (x0 x7 x9)x0 x8 x9x10)x10
Definition 6f07c.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (a3794.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9(x1 = x10∀ x12 : ο . x12)(x2 = x10∀ x12 : ο . x12)(x3 = x10∀ x12 : ο . x12)(x4 = x10∀ x12 : ο . x12)(x5 = x10∀ x12 : ο . x12)(x6 = x10∀ x12 : ο . x12)(x7 = x10∀ x12 : ο . x12)(x8 = x10∀ x12 : ο . x12)(x9 = x10∀ x12 : ο . x12)x0 x1 x10x0 x2 x10not (x0 x3 x10)not (x0 x4 x10)x0 x5 x10not (x0 x6 x10)not (x0 x7 x10)x0 x8 x10not (x0 x9 x10)x11)x11
Definition f7297.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (6f07c.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10(x1 = x11∀ x13 : ο . x13)(x2 = x11∀ x13 : ο . x13)(x3 = x11∀ x13 : ο . x13)(x4 = x11∀ x13 : ο . x13)(x5 = x11∀ x13 : ο . x13)(x6 = x11∀ x13 : ο . x13)(x7 = x11∀ x13 : ο . x13)(x8 = x11∀ x13 : ο . x13)(x9 = x11∀ x13 : ο . x13)(x10 = x11∀ x13 : ο . x13)x0 x1 x11not (x0 x2 x11)not (x0 x3 x11)not (x0 x4 x11)x0 x5 x11not (x0 x6 x11)not (x0 x7 x11)not (x0 x8 x11)not (x0 x9 x11)not (x0 x10 x11)x12)x12
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)
Definition oror := λ x0 x1 : ο . ∀ x2 : ο . (x0x2)(x1x2)x2
Known xmxm : ∀ x0 : ο . or x0 (not x0)
Known FalseEFalseE : False∀ x0 : ο . x0
Known 53a3c.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0not (x1 x2 x3)not (x1 x3 x2))cf2df.. x0 x1∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0(x2 = x3∀ x7 : ο . x7)(x2 = x4∀ x7 : ο . x7)(x3 = x4∀ x7 : ο . x7)(x2 = x5∀ x7 : ο . x7)(x3 = x5∀ x7 : ο . x7)(x4 = x5∀ x7 : ο . x7)(x2 = x6∀ x7 : ο . x7)(x3 = x6∀ x7 : ο . x7)(x4 = x6∀ x7 : ο . x7)(x5 = x6∀ x7 : ο . x7)not (x1 x2 x3)not (x1 x2 x4)not (x1 x3 x4)not (x1 x2 x5)not (x1 x3 x5)not (x1 x4 x5)not (x1 x2 x6)not (x1 x3 x6)not (x1 x4 x6)not (x1 x5 x6)False
Known 61345.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)4402e.. x0 x1∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0(x2 = x3∀ x5 : ο . x5)(x2 = x4∀ x5 : ο . x5)(x3 = x4∀ x5 : ο . x5)x1 x2 x3x1 x2 x4x1 x3 x4False
Known Subq_traSubq_tra : ∀ x0 x1 x2 . x0x1x1x2x0x2
Known setminus_Subqsetminus_Subq : ∀ x0 x1 . setminus x0 x1x0
Known SingISingI : ∀ x0 . x0Sing x0
Theorem 2c796.. : ∀ 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 . x11x0∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0f7297.. x2 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14∀ x15 : ο . (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 x3not (x2 x12 x3)not (x2 x13 x3)x2 x14 x3x15)(not (x2 x4 x3)x2 x5 x3x2 x6 x3not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x2 x11 x3not (x2 x12 x3)not (x2 x13 x3)x2 x14 x3x15)(not (x2 x4 x3)x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)x2 x10 x3x2 x11 x3not (x2 x12 x3)not (x2 x13 x3)x2 x14 x3x15)x15 (proof)