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Proofgold Signed Transaction

vin
PrKTn../7fbb6..
PUSWj../f99fc..
vout
PrKTn../289d8.. 6.00 bars
TMaPN../dc01d.. ownership of 0a100.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
TMLAy../dff21.. ownership of c4edd.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
PUeBH../962d4.. doc published by Pr4zB..
Param 4402e.. : ι(ιιο) → ο
Param cf2df.. : ι(ιιο) → ο
Definition SubqSubq := λ x0 x1 . ∀ x2 . x2x0x2x1
Param setminussetminus : ιιι
Param SingSing : ιι
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Definition 8b6ad.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 . ∀ x5 : ο . ((x1 = x2∀ x6 : ο . x6)(x1 = x3∀ x6 : ο . x6)(x2 = x3∀ x6 : ο . x6)(x1 = x4∀ x6 : ο . x6)(x2 = x4∀ x6 : ο . x6)(x3 = x4∀ x6 : ο . x6)not (x0 x1 x2)not (x0 x1 x3)not (x0 x2 x3)not (x0 x1 x4)not (x0 x2 x4)not (x0 x3 x4)x5)x5
Definition c5756.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 . ∀ x6 : ο . (8b6ad.. x0 x1 x2 x3 x4(x1 = x5∀ x7 : ο . x7)(x2 = x5∀ x7 : ο . x7)(x3 = x5∀ x7 : ο . x7)(x4 = x5∀ x7 : ο . x7)not (x0 x1 x5)not (x0 x2 x5)x0 x3 x5x0 x4 x5x6)x6
Definition ba720.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (c5756.. x0 x1 x2 x3 x4 x5(x1 = x6∀ x8 : ο . x8)(x2 = x6∀ x8 : ο . x8)(x3 = x6∀ x8 : ο . x8)(x4 = x6∀ x8 : ο . x8)(x5 = x6∀ x8 : ο . x8)x0 x1 x6x0 x2 x6not (x0 x3 x6)x0 x4 x6not (x0 x5 x6)x7)x7
Definition 6ca1f.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (ba720.. x0 x1 x2 x3 x4 x5 x6(x1 = x7∀ x9 : ο . x9)(x2 = x7∀ x9 : ο . x9)(x3 = x7∀ x9 : ο . x9)(x4 = x7∀ x9 : ο . x9)(x5 = x7∀ x9 : ο . x9)(x6 = x7∀ x9 : ο . x9)x0 x1 x7x0 x2 x7x0 x3 x7not (x0 x4 x7)not (x0 x5 x7)not (x0 x6 x7)x8)x8
Definition d8761.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (6ca1f.. 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)not (x0 x1 x8)not (x0 x2 x8)x0 x3 x8x0 x4 x8not (x0 x5 x8)not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition 0b765.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (6ca1f.. 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)not (x0 x1 x8)x0 x2 x8not (x0 x3 x8)not (x0 x4 x8)not (x0 x5 x8)not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition a6296.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (0b765.. 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)not (x0 x1 x9)not (x0 x2 x9)x0 x3 x9x0 x4 x9not (x0 x5 x9)not (x0 x6 x9)not (x0 x7 x9)x0 x8 x9x10)x10
Definition 1b190.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (6ca1f.. 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
Definition 4e4f8.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (1b190.. 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)not (x0 x1 x9)not (x0 x2 x9)x0 x3 x9x0 x4 x9not (x0 x5 x9)not (x0 x6 x9)not (x0 x7 x9)x0 x8 x9x10)x10
Definition 6661c.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 . ∀ x10 : ο . (d8761.. 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 x9x0 x2 x9not (x0 x3 x9)not (x0 x4 x9)x0 x5 x9not (x0 x6 x9)not (x0 x7 x9)x0 x8 x9x10)x10
Definition andand := λ x0 x1 : ο . ∀ x2 : ο . (x0x1x2)x2
Definition nInnIn := λ x0 x1 . not (x0x1)
Known setminusEsetminusE : ∀ x0 x1 x2 . x2setminus x0 x1and (x2x0) (nIn x2 x1)
Known 29f8c.. : ∀ x0 x1 . ∀ x2 : ι → ι → ο . (∀ x3 . x3x1∀ x4 . x4x1x2 x3 x4x2 x4 x3)4402e.. x1 x2cf2df.. x1 x2∀ x3 . x3x1x0setminus x1 (Sing x3)∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0∀ x8 . x8x0∀ x9 . x9x0∀ x10 . x10x0∀ x11 . x11x0d8761.. x2 x4 x5 x6 x7 x8 x9 x10 x11∀ x12 : ο . (x2 x4 x3not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)not (x2 x11 x3)x12)(not (x2 x4 x3)x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)not (x2 x11 x3)x12)(x2 x4 x3x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)not (x2 x11 x3)x12)(x2 x4 x3not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x2 x11 x3x12)(not (x2 x4 x3)x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x2 x11 x3x12)(x2 x4 x3x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x2 x11 x3x12)(x2 x4 x3not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)x2 x11 x3x12)(not (x2 x4 x3)x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)x2 x11 x3x12)(x2 x4 x3x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)x2 x11 x3x12)x12
Known d7596.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x08b6ad.. x1 x2 x3 x4 x58b6ad.. x1 x3 x2 x4 x5
Known neq_i_symneq_i_sym : ∀ x0 x1 . (x0 = x1∀ x2 : ο . x2)x1 = x0∀ x2 : ο . x2
Known 868dd.. : ∀ 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 . x8x06ca1f.. x1 x2 x3 x4 x5 x6 x7 x86ca1f.. x1 x3 x2 x4 x5 x6 x7 x8
Known 02118.. : ∀ 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 . x9x0d8761.. x1 x2 x3 x4 x5 x6 x7 x8 x9d8761.. x1 x9 x6 x8 x7 x3 x5 x4 x2
Known Subq_traSubq_tra : ∀ x0 x1 x2 . x0x1x1x2x0x2
Known setminus_Subqsetminus_Subq : ∀ x0 x1 . setminus x0 x1x0
Known SingISingI : ∀ x0 . x0Sing x0
Theorem 0a100.. : ∀ x0 x1 . ∀ x2 : ι → ι → ο . (∀ x3 . x3x1∀ x4 . x4x1x2 x3 x4x2 x4 x3)4402e.. x1 x2cf2df.. x1 x2∀ x3 . x3x1x0setminus x1 (Sing x3)∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0∀ x8 . x8x0∀ x9 . x9x0∀ x10 . x10x0∀ x11 . x11x0d8761.. x2 x4 x5 x6 x7 x8 x9 x10 x11∀ x12 : ο . (∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0∀ x19 . x19x0∀ x20 . x20x0a6296.. x2 x13 x14 x15 x16 x17 x18 x19 x3 x20x12)(∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0∀ x19 . x19x0∀ x20 . x20x04e4f8.. x2 x13 x14 x15 x16 x17 x18 x19 x3 x20x12)(∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0∀ x19 . x19x0∀ x20 . x20x06661c.. x2 x13 x14 x15 x16 x17 x18 x19 x20 x3x12)x12 (proof)