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Proofgold Asset

asset id
633e432003da78a1bacdeddb26706bb82dcb8d55524df69a68251893ecfcb804
asset hash
e9aaae89dff9d5d73d4adc3014da8130af877aa7909b19d730867c25e01f25d4
bday / block
35843
tx
21089..
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 f8709.. := 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 x6x0 x3 x6x0 x4 x6not (x0 x5 x6)x7)x7
Definition 27260.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (f8709.. 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 x7not (x0 x3 x7)not (x0 x4 x7)x0 x5 x7not (x0 x6 x7)x8)x8
Definition dfcf9.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (27260.. 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 c4d5c.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (dfcf9.. 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)not (x0 x3 x9)x0 x4 x9not (x0 x5 x9)not (x0 x6 x9)not (x0 x7 x9)x0 x8 x9x10)x10
Definition 3a344.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (c4d5c.. 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 x10not (x0 x2 x10)x0 x3 x10x0 x4 x10not (x0 x5 x10)not (x0 x6 x10)not (x0 x7 x10)x0 x8 x10not (x0 x9 x10)x11)x11
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 90ee6.. : ∀ 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 . x13x03a344.. x2 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13∀ x14 : ο . (x2 x4 x3not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3x2 x9 x3not (x2 x10 x3)x2 x11 x3not (x2 x12 x3)not (x2 x13 x3)x14)x14 (proof)