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Proofgold Signed Transaction

vin
PrDs8../a8178..
PUeux../cd73f..
vout
PrDs8../6a5a9.. 6.12 bars
TMThc../a39bd.. ownership of 53b7a.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
TMQgd../463c1.. ownership of aa769.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
PUXdn../abd9e.. doc published by Pr4zB..
Param 8c395.. : (ιιο) → ιιιιιιιο
Param notnot : οο
Definition e37d4.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (8c395.. 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)x0 x1 x8x0 x2 x8not (x0 x3 x8)not (x0 x4 x8)not (x0 x5 x8)not (x0 x6 x8)not (x0 x7 x8)x9)x9
Known 05116.. : ∀ 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 . x8x08c395.. x1 x2 x3 x4 x5 x6 x7 x88c395.. x1 x2 x3 x4 x6 x5 x7 x8
Theorem 53b7a.. : ∀ 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 . x9x0e37d4.. x1 x2 x3 x4 x5 x6 x7 x8 x9e37d4.. x1 x2 x3 x4 x6 x5 x7 x8 x9 (proof)