Step 
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 of Lemma 
shadow-inequalities_wf
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∀[n:ℕ]. ∀[ineqs:{L:ℤ List| ||L|| = n ∈ ℤ}  List]. ∀[i:ℕn].
  (shadow-inequalities(i;ineqs) ∈ {L:ℤ List| ||L|| = (n - 1) ∈ ℤ}  List)
BY
 
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1. n : ℕ
2. ineqs : {L:ℤ List| ||L|| = n ∈ ℤ}  List
3. i : ℕn
⊢ shadow-inequalities(i;ineqs) ∈ {L:ℤ List| ||L|| = (n - 1) ∈ ℤ}  List
 
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\mforall{}[n:\mBbbN{}].  \mforall{}[ineqs:\{L:\mBbbZ{}  List|  ||L||  =  n\}    List].  \mforall{}[i:\mBbbN{}n].
    (shadow-inequalities(i;ineqs)  \mmember{}  \{L:\mBbbZ{}  List|  ||L||  =  (n  -  1)\}    List)
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