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Proofgold Signed Transaction

vin
Pr9uB../e00fd..
PUZjB../71d3b..
vout
Pr9uB../7b2de.. 18.66 bars
TMciF../b81b5.. ownership of 4832f.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
TMde9../2cbb7.. ownership of 8ab02.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
PUW4r../025e0.. 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 21422.. := 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 x7not (x0 x4 x7)not (x0 x5 x7)x0 x6 x7x8)x8
Definition f0d5b.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (21422.. 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 8f55d.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (f0d5b.. 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)x0 x2 x9not (x0 x3 x9)not (x0 x4 x9)x0 x5 x9not (x0 x6 x9)x0 x7 x9x0 x8 x9x10)x10
Definition b1def.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . ∀ x11 : ο . (8f55d.. 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 x10not (x0 x4 x10)not (x0 x5 x10)not (x0 x6 x10)not (x0 x7 x10)x0 x8 x10not (x0 x9 x10)x11)x11
Definition df932.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (b1def.. 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 x11x0 x2 x11x0 x3 x11not (x0 x4 x11)not (x0 x5 x11)not (x0 x6 x11)not (x0 x7 x11)x0 x8 x11not (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 4832f.. : ∀ 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 . x14x0df932.. x2 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14∀ x15 : ο . x15 (proof)