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


1. f : ℤ ⟶ ℤ
2. L2 : polynomial-constraints() List
3. L1 : polynomial-constraints() List
4. X1 : polynomial-constraints()
5. (X1 ∈ L1)
6. satisfies-poly-constraints(f;X1)
7. X : polynomial-constraints()
8. (X ∈ L2)
9. satisfies-poly-constraints(f;X)
⊢ ∃X:polynomial-constraints()
   ((∃A:polynomial-constraints()
      ((A ∈ L1) ∧ (∃B:polynomial-constraints(). ((B ∈ L2) ∧ (X = combine-pcs(A;B) ∈ polynomial-constraints())))))
   ∧ satisfies-poly-constraints(f;X))
BY
{ (With ⌜combine-pcs(X1;X)⌝ (D 0)⋅ THEN Auto THEN BLemma `satisfies-combine-pcs` THEN Auto) }

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Latex:

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Latex:

1.  f  :  \mBbbZ{}  {}\mrightarrow{}  \mBbbZ{}
2.  L2  :  polynomial-constraints()  List
3.  L1  :  polynomial-constraints()  List
4.  X1  :  polynomial-constraints()
5.  (X1  \mmember{}  L1)
6.  satisfies-poly-constraints(f;X1)
7.  X  :  polynomial-constraints()
8.  (X  \mmember{}  L2)
9.  satisfies-poly-constraints(f;X)
\mvdash{}  \mexists{}X:polynomial-constraints()
      ((\mexists{}A:polynomial-constraints()
            ((A  \mmember{}  L1)  \mwedge{}  (\mexists{}B:polynomial-constraints().  ((B  \mmember{}  L2)  \mwedge{}  (X  =  combine-pcs(A;B))))))
      \mwedge{}  satisfies-poly-constraints(f;X))


By

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Latex:
(With  \mkleeneopen{}combine-pcs(X1;X)\mkleeneclose{}  (D  0)\mcdot{}  THEN  Auto  THEN  BLemma  `satisfies-combine-pcs`  THEN  Auto)

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