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Proofgold Signed Transaction

vin
Pr8YJ../c1bb3..
PUgrK../c3eeb..
vout
Pr8YJ../39290.. 19.97 bars
TMKod../029ed.. ownership of 801dc.. as prop with payaddr Pr6Pc.. rights free controlledby Pr6Pc.. upto 0
TMQvj../518a8.. ownership of e406c.. as prop with payaddr Pr6Pc.. rights free controlledby Pr6Pc.. upto 0
PUd4j../e57be.. doc published by Pr6Pc..
Definition andand := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2
Param explicit_Field_minusexplicit_Field_minus : ι → ι → ι → (ι → ι → ι) → (ι → ι → ι) → ι → ι
Param ReplSep2ReplSep2 : ι → (ι → ι) → (ι → ι → ο) → CT2 ι
Param TrueTrue : ο
Known andIandI : ∀ x0 x1 : ο . x0 ⟶ x1 ⟶ and x0 x1
Definition FalseFalse := ∀ x0 : ο . x0
Theorem 801dc.. : ∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x3 x7 x8 ∈ x0) ⟶ x1 ∈ x0 ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x4 x7 x8 ∈ x0) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ x4 x7 (x4 x8 x9) = x4 (x4 x7 x8) x9) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x4 x7 x8 = x4 x8 x7) ⟶ x2 ∈ x0 ⟶ (∀ x7 . x7 ∈ x0 ⟶ (x7 = x1 ⟶ ∀ x8 : ο . x8) ⟶ ∃ x8 . and (x8 ∈ x0) (x4 x7 x8 = x2)) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ x4 x7 (x3 x8 x9) = x3 (x4 x7 x8) (x4 x7 x9)) ⟶ (∀ x7 . x7 ∈ x0 ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x7 ∈ x0) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ ∀ x9 . x9 ∈ x0 ⟶ x4 (x3 x7 x8) x9 = x3 (x4 x7 x9) (x4 x8 x9)) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ explicit_Field_minus x0 x1 x2 x3 x4 (x3 x7 x8) = x3 (explicit_Field_minus x0 x1 x2 x3 x4 x7) (explicit_Field_minus x0 x1 x2 x3 x4 x8)) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x4 (explicit_Field_minus x0 x1 x2 x3 x4 x7) x8 = explicit_Field_minus x0 x1 x2 x3 x4 (x4 x7 x8)) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x4 x7 (explicit_Field_minus x0 x1 x2 x3 x4 x8) = explicit_Field_minus x0 x1 x2 x3 x4 (x4 x7 x8)) ⟶ (∀ x7 . x7 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ prim0 (λ x8 . and (x8 ∈ x0) (∃ x9 . and (x9 ∈ x0) (x7 = x6 x8 x9))) ∈ x0) ⟶ (∀ x7 . x7 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ prim0 (λ x8 . and (x8 ∈ x0) (x7 = x6 (prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x7 = x6 x10 x11)))) x8)) ∈ x0) ⟶ (∀ x7 . x7 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ ∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x7 = x6 x10 x11))) = prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x8 = x6 x10 x11))) ⟶ prim0 (λ x10 . and (x10 ∈ x0) (x7 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x7 = x6 x12 x13)))) x10)) = prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x8 = x6 x12 x13)))) x10)) ⟶ x7 = x8) ⟶ (∀ x7 . x7 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ ∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ x6 (x3 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (∃ x10 . and (x10 ∈ x0) (x7 = x6 x9 x10)))) (prim0 (λ x9 . and (x9 ∈ x0) (∃ x10 . and (x10 ∈ x0) (x8 = x6 x9 x10))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x7 = x6 x11 x12)))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) x9)))))) (x3 (x4 (prim0 (λ x9 . and (x9 ∈ x0) (∃ x10 . and (x10 ∈ x0) (x7 = x6 x9 x10)))) (prim0 (λ x9 . and (x9 ∈ x0) (x8 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))) x9)))) (x4 (prim0 (λ x9 . and (x9 ∈ x0) (x7 = x6 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x7 = x6 x11 x12)))) x9))) (prim0 (λ x9 . and (x9 ∈ x0) (∃ x10 . and (x10 ∈ x0) (x8 = x6 x9 x10)))))) ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ (∀ x7 . x7 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ ∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x6 (x3 (x4 (prim0 (λ x14 . and (x14 ∈ x0) (∃ x15 . and (x15 ∈ x0) (x7 = x6 x14 x15)))) (prim0 (λ x14 . and (x14 ∈ x0) (∃ x15 . and (x15 ∈ x0) (x8 = x6 x14 x15))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x14 . and (x14 ∈ x0) (x7 = x6 (prim0 (λ x16 . and (x16 ∈ x0) (∃ x17 . and (x17 ∈ x0) (x7 = x6 x16 x17)))) x14))) (prim0 (λ x14 . and (x14 ∈ x0) (x8 = x6 (prim0 (λ x16 . and (x16 ∈ x0) (∃ x17 . and (x17 ∈ x0) (x8 = x6 x16 x17)))) x14)))))) (x3 (x4 (prim0 (λ x14 . and (x14 ∈ x0) (∃ x15 . and (x15 ∈ x0) (x7 = x6 x14 x15)))) (prim0 (λ x14 . and (x14 ∈ x0) (x8 = x6 (prim0 (λ x16 . and (x16 ∈ x0) (∃ x17 . and (x17 ∈ x0) (x8 = x6 x16 x17)))) x14)))) (x4 (prim0 (λ x14 . and (x14 ∈ x0) (x7 = x6 (prim0 (λ x16 . and (x16 ∈ x0) (∃ x17 . and (x17 ∈ x0) (x7 = x6 x16 x17)))) x14))) (prim0 (λ x14 . and (x14 ∈ x0) (∃ x15 . and (x15 ∈ x0) (x8 = x6 x14 x15)))))) = x6 x10 x11))) = x3 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x7 = x6 x10 x11)))) (prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x8 = x6 x10 x11))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (x7 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x7 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x8 = x6 x12 x13)))) x10)))))) ⟶ (∀ x7 . x7 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ ∀ x8 . x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6 ⟶ prim0 (λ x10 . and (x10 ∈ x0) (x6 (x3 (x4 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x7 = x6 x12 x13)))) (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x8 = x6 x12 x13))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x12 . and (x12 ∈ x0) (x7 = x6 (prim0 (λ x14 . and (x14 ∈ x0) (∃ x15 . and (x15 ∈ x0) (x7 = x6 x14 x15)))) x12))) (prim0 (λ x12 . and (x12 ∈ x0) (x8 = x6 (prim0 (λ x14 . and (x14 ∈ x0) (∃ x15 . and (x15 ∈ x0) (x8 = x6 x14 x15)))) x12)))))) (x3 (x4 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x7 = x6 x12 x13)))) (prim0 (λ x12 . and (x12 ∈ x0) (x8 = x6 (prim0 (λ x14 . and (x14 ∈ x0) (∃ x15 . and (x15 ∈ x0) (x8 = x6 x14 x15)))) x12)))) (x4 (prim0 (λ x12 . and (x12 ∈ x0) (x7 = x6 (prim0 (λ x14 . and (x14 ∈ x0) (∃ x15 . and (x15 ∈ x0) (x7 = x6 x14 x15)))) x12))) (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x8 = x6 x12 x13)))))) = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x6 (x3 (x4 (prim0 (λ x16 . and (x16 ∈ x0) (∃ x17 . and (x17 ∈ x0) (x7 = x6 x16 x17)))) (prim0 (λ x16 . and (x16 ∈ x0) (∃ x17 . and (x17 ∈ x0) (x8 = x6 x16 x17))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x16 . and (x16 ∈ x0) (x7 = x6 (prim0 (λ x18 . and (x18 ∈ x0) (∃ x19 . and (x19 ∈ x0) (x7 = x6 x18 x19)))) x16))) (prim0 (λ x16 . and (x16 ∈ x0) (x8 = x6 (prim0 (λ x18 . and (x18 ∈ x0) (∃ x19 . and (x19 ∈ x0) (x8 = x6 x18 x19)))) x16)))))) (x3 (x4 (prim0 (λ x16 . and (x16 ∈ x0) (∃ x17 . and (x17 ∈ x0) (x7 = x6 x16 x17)))) (prim0 (λ x16 . and (x16 ∈ x0) (x8 = x6 (prim0 (λ x18 . and (x18 ∈ x0) (∃ x19 . and (x19 ∈ x0) (x8 = x6 x18 x19)))) x16)))) (x4 (prim0 (λ x16 . and (x16 ∈ x0) (x7 = x6 (prim0 (λ x18 . and (x18 ∈ x0) (∃ x19 . and (x19 ∈ x0) (x7 = x6 x18 x19)))) x16))) (prim0 (λ x16 . and (x16 ∈ x0) (∃ x17 . and (x17 ∈ x0) (x8 = x6 x16 x17)))))) = x6 x12 x13)))) x10)) = x3 (x4 (prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x7 = x6 x10 x11)))) (prim0 (λ x10 . and (x10 ∈ x0) (x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x8 = x6 x12 x13)))) x10)))) (x4 (prim0 (λ x10 . and (x10 ∈ x0) (x7 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x7 = x6 x12 x13)))) x10))) (prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x8 = x6 x10 x11)))))) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x6 x7 x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ prim0 (λ x10 . and (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x6 x7 x8 = x6 x10 x11))) = x7) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ prim0 (λ x10 . and (x10 ∈ x0) (x6 x7 x8 = x6 (prim0 (λ x12 . and (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x6 x7 x8 = x6 x12 x13)))) x10)) = x8) ⟶ x6 x1 x1 ∈ ReplSep2 x0 (λ x7 . x0) (λ x7 x8 . True) x6 ⟶ x6 x2 x1 ∈ ReplSep2 x0 (λ x7 . x0) (λ x7 x8 . True) x6 ⟶ (∀ x7 . x7 ∈ x0 ⟶ explicit_Field_minus x0 x1 x2 x3 x4 (explicit_Field_minus x0 x1 x2 x3 x4 x7) = x7) ⟶ (∀ x7 . x7 ∈ x0 ⟶ x3 (explicit_Field_minus x0 x1 x2 x3 x4 x7) x7 = x1) ⟶ (∀ x7 . x7 ∈ x0 ⟶ x4 x1 x7 = x1) ⟶ (∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x3 (x4 x7 x7) (x4 x8 x8) = x1 ⟶ and (x7 = x1) (x8 = x1)) ⟶ ∀ x7 . x7 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ (x7 = x6 x1 x1 ⟶ ∀ x8 : ο . x8) ⟶ ∃ x8 . and (x8 ∈ ReplSep2 x0 (λ x10 . x0) (λ x10 x11 . True) x6) (x6 (x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x7 = x6 x11 x12)))) (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12))))) (explicit_Field_minus x0 x1 x2 x3 x4 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x7 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x7 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) x11)))))) (x3 (x4 (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x7 = x6 x11 x12)))) (prim0 (λ x11 . and (x11 ∈ x0) (x8 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x8 = x6 x13 x14)))) x11)))) (x4 (prim0 (λ x11 . and (x11 ∈ x0) (x7 = x6 (prim0 (λ x13 . and (x13 ∈ x0) (∃ x14 . and (x14 ∈ x0) (x7 = x6 x13 x14)))) x11))) (prim0 (λ x11 . and (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x8 = x6 x11 x12)))))) = x6 x2 x1)
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