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Proofgold Signed Transaction

vin
Pr3UG../bf356..
PUcXD../5f2eb..
vout
Pr3UG../e049d.. 12.35 bars
TMTsU../62e6d.. ownership of cc4c2.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
TMQnR../596fe.. ownership of 8b169.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
PUQ8A../5d0f6.. doc published by Pr4zB..
Param c1515.. : (ιιο) → ιιιιιιιιο
Known 4730e.. : ∀ 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 . x9x0c1515.. x1 x2 x3 x4 x5 x6 x7 x8 x9c1515.. x1 x2 x3 x5 x4 x6 x7 x8 x9
Known 0bc98.. : ∀ 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 . x9x0c1515.. x1 x2 x3 x4 x5 x6 x7 x8 x9c1515.. x1 x2 x3 x4 x5 x7 x6 x8 x9
Theorem cc4c2.. : ∀ 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 . x9x0c1515.. x1 x2 x3 x4 x5 x6 x7 x8 x9c1515.. x1 x2 x3 x5 x4 x7 x6 x8 x9 (proof)