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Step * of Lemma alpha-rename_wf

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∀[opr:Type]. ∀[t:term(opr)].
  ∀f:{v:varname()| (v ∈ all-vars(t))}  ⟶ varname()
    alpha-rename(f;t) ∈ term(opr) 
    supposing ∀x:{v:varname()| (v ∈ all-vars(t))} . (((f x) = nullvar() ∈ varname()) ⇒ (x = nullvar() ∈ varname()))
BY
{ ProveWfLemma }

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Latex:

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Latex:
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\mforall{}[opr:Type].  \mforall{}[t:term(opr)].
    \mforall{}f:\{v:varname()|  (v  \mmember{}  all-vars(t))\}    {}\mrightarrow{}  varname()
        alpha-rename(f;t)  \mmember{}  term(opr) 
        supposing  \mforall{}x:\{v:varname()|  (v  \mmember{}  all-vars(t))\}  .  (((f  x)  =  nullvar())  {}\mRightarrow{}  (x  =  nullvar()))


By

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Latex:
ProveWfLemma

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