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Step * 1 1 of Lemma satisfies-negate-poly-constraints


1. f : ℤ ⟶ ℤ
⊢ (∃X∈negate-poly-constraints([]). satisfies-poly-constraints(f;X))
⇐⇒ (∀X∈[].(∃Z∈negate-poly-constraint(X). satisfies-poly-constraints(f;Z)))
BY
{ (RepUR ``negate-poly-constraints`` 0
   THEN (RWO "l_all_nil_iff l_exists_single" 0 THENA Auto)
   THEN RepUR ``satisfies-poly-constraints`` 0
   THEN RWO "l_all_nil_iff" 0
   THEN Auto) }

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Latex:

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Latex:

1.  f  :  \mBbbZ{}  {}\mrightarrow{}  \mBbbZ{}
\mvdash{}  (\mexists{}X\mmember{}negate-poly-constraints([]).  satisfies-poly-constraints(f;X))
\mLeftarrow{}{}\mRightarrow{}  (\mforall{}X\mmember{}[].(\mexists{}Z\mmember{}negate-poly-constraint(X).  satisfies-poly-constraints(f;Z)))


By

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Latex:
(RepUR  ``negate-poly-constraints``  0
  THEN  (RWO  "l\_all\_nil\_iff  l\_exists\_single"  0  THENA  Auto)
  THEN  RepUR  ``satisfies-poly-constraints``  0
  THEN  RWO  "l\_all\_nil\_iff"  0
  THEN  Auto)

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