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Proofgold Signed Transaction

vin
Pr9DE../34dcd..
PUMa8../148c6..
vout
Pr9DE../87836.. 24.99 bars
TMSy7../7f71f.. ownership of 2ecf9.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
TMT4b../3c81d.. ownership of ba483.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
PULKE../a0562.. doc published by Pr4zB..
Param dfcf9.. : (ιιο) → ιιιιιιιιο
Param notnot : οο
Definition 8d9b1.. := 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)not (x0 x4 x9)not (x0 x5 x9)x0 x6 x9not (x0 x7 x9)x0 x8 x9x10)x10
Known eff2b.. : ∀ 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 . x9x0dfcf9.. x1 x2 x3 x4 x5 x6 x7 x8 x9dfcf9.. x1 x2 x3 x5 x4 x6 x7 x8 x9
Theorem 2ecf9.. : ∀ 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 . x9x0∀ x10 . x10x08d9b1.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x108d9b1.. x1 x2 x3 x5 x4 x6 x7 x8 x9 x10 (proof)