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Proofgold Signed Transaction

vin
Pr8XD../f773f..
PUf28../6b4c9..
vout
Pr8XD../d707b.. 25.00 bars
TMNZd../9a192.. ownership of 342e6.. as prop with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0
TMFjb../f6d59.. ownership of 3397f.. as prop with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0
PUYzn../8bda5.. doc published by Pr4zB..
Param f1c88.. : (ιιο) → ιιιιιιιιιιο
Param notnot : οο
Definition df3c6.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . ∀ x12 : ο . (f1c88.. x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10(x1 = x11∀ x13 : ο . x13)(x2 = x11∀ x13 : ο . x13)(x3 = x11∀ x13 : ο . x13)(x4 = x11∀ x13 : ο . x13)(x5 = x11∀ x13 : ο . x13)(x6 = x11∀ x13 : ο . x13)(x7 = x11∀ x13 : ο . x13)(x8 = x11∀ x13 : ο . x13)(x9 = x11∀ x13 : ο . x13)(x10 = x11∀ x13 : ο . x13)not (x0 x1 x11)x0 x2 x11x0 x3 x11not (x0 x4 x11)not (x0 x5 x11)not (x0 x6 x11)not (x0 x7 x11)x0 x8 x11not (x0 x9 x11)not (x0 x10 x11)x12)x12
Known 9a7a5.. : ∀ 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 . x10x0∀ x11 . x11x0f1c88.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11f1c88.. x1 x2 x4 x3 x5 x7 x6 x8 x9 x11 x10
Theorem 342e6.. : ∀ 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 . x10x0∀ x11 . x11x0∀ x12 . x12x0df3c6.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12df3c6.. x1 x2 x4 x3 x5 x7 x6 x8 x9 x11 x10 x12 (proof)