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Proofgold Signed Transaction

vin
PrNHV../07b04..
PUbDM../7527c..
vout
PrNHV../22306.. 6.13 bars
TMZzt../f070d.. ownership of 4c0f6.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
TMb1c../6651c.. ownership of d35f1.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
PUSZK../fdb3b.. doc published by Pr4zB..
Param b0193.. : (ιιο) → ιιιιιιιο
Param notnot : οο
Definition 55a2d.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (b0193.. 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
Known cf2d6.. : ∀ 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 . x8x0b0193.. x1 x2 x3 x4 x5 x6 x7 x8b0193.. x1 x3 x2 x4 x5 x6 x7 x8
Theorem 4c0f6.. : ∀ 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 . x9x055a2d.. x1 x2 x3 x4 x5 x6 x7 x8 x955a2d.. x1 x3 x2 x4 x5 x6 x7 x8 x9 (proof)