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Proofgold Signed Transaction

vin
PrAwE../ffc6e..
PUYYM../f1875..
vout
PrAwE../d27c1.. 25.00 bars
TMZwt../f24b5.. ownership of 178b1.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
TMcQR../7d596.. ownership of 166fc.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
PUThB../edbc8.. doc published by Pr4zB..
Param e4c05.. : (ιιο) → ιιιιιιιιο
Known efcc9.. : ∀ 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 . x9x0e4c05.. x1 x2 x3 x4 x5 x6 x7 x8 x9e4c05.. x1 x2 x4 x3 x5 x6 x7 x8 x9
Known f033d.. : ∀ 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 . x9x0e4c05.. x1 x2 x3 x4 x5 x6 x7 x8 x9e4c05.. x1 x2 x3 x4 x5 x6 x8 x7 x9
Theorem 178b1.. : ∀ 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 . x9x0e4c05.. x1 x2 x3 x4 x5 x6 x7 x8 x9e4c05.. x1 x2 x4 x3 x5 x6 x8 x7 x9 (proof)