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Step * of Lemma mFOL-rename-bound-to-avoid_wf

∀fmla:mFOL(). ∀L:ℤ List.
  (mFOL-rename-bound-to-avoid(fmla;L) ∈ {fmla':mFOL()| 
                                         (mFOL-abstract(fmla') = mFOL-abstract(fmla) ∈ AbstractFOFormula)
                                         ∧ l_disjoint(ℤ;L;mFOL-boundvars(fmla'))} )
BY
{ (Auto
   THEN RW  (AddrC [2] UnfoldTopAbC) 0
   THEN Subst ⌈TERMOF{mFOL-bound-rename:o, 1:l, 1:l} ~ TERMOF{mFOL-bound-rename:o, 1:l, i:l}⌉ 0⋅) }

1
.....equality..... 
1. fmla : mFOL()@i
2. L : ℤ List@i
⊢ TERMOF{mFOL-bound-rename:o, 1:l, 1:l} ~ TERMOF{mFOL-bound-rename:o, 1:l, i:l}

2
1. fmla : mFOL()@i
2. L : ℤ List@i
⊢ TERMOF{mFOL-bound-rename:o, 1:l, i:l} fmla L ∈ {fmla':mFOL()| 
                                                  (mFOL-abstract(fmla') = mFOL-abstract(fmla) ∈ AbstractFOFormula)
                                                  ∧ l_disjoint(ℤ;L;mFOL-boundvars(fmla'))} 

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Latex:


\mforall{}fmla:mFOL().  \mforall{}L:\mBbbZ{}  List.
    (mFOL-rename-bound-to-avoid(fmla;L)  \mmember{}  \{fmla':mFOL()| 
                                                                                  (mFOL-abstract(fmla')  =  mFOL-abstract(fmla))
                                                                                  \mwedge{}  l\_disjoint(\mBbbZ{};L;mFOL-boundvars(fmla'))\}  )


By

(Auto
  THEN  RW    (AddrC  [2]  UnfoldTopAbC)  0
  THEN  Subst  \mkleeneopen{}TERMOF\{mFOL-bound-rename:o,  1:l,  1:l\}  \msim{}  TERMOF\{mFOL-bound-rename:o,  1:l,  i:l\}\mkleeneclose{}  0\mcdot{})

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