Nuprl Lemma : FOL-rename-bound-to-avoid_wf
∀fmla:mFOL(). ∀L:ℤ List.
  (FOL-rename-bound-to-avoid(fmla;L) ∈ {fmla':mFOL()| 
                                        (mFOL-freevars(fmla') = mFOL-freevars(fmla) ∈ (ℤ List))
                                        ∧ (FOL-abstract(fmla')
                                          = FOL-abstract(fmla)
                                          ∈ AbstractFOFormula+(mFOL-freevars(fmla)))
                                        ∧ l_disjoint(ℤ;L;mFOL-boundvars(fmla'))} )
Proof
Definitions occuring in Statement : 
FOL-rename-bound-to-avoid: FOL-rename-bound-to-avoid(fmla;L)
, 
FOL-abstract: FOL-abstract(fmla)
, 
mFOL-boundvars: mFOL-boundvars(fmla)
, 
mFOL-freevars: mFOL-freevars(fmla)
, 
mFOL: mFOL()
, 
AbstractFOFormula+: AbstractFOFormula+(vs)
, 
l_disjoint: l_disjoint(T;l1;l2)
, 
list: T List
, 
all: ∀x:A. B[x]
, 
and: P ∧ Q
, 
member: t ∈ T
, 
set: {x:A| B[x]} 
, 
int: ℤ
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
FOL-rename-bound-to-avoid: FOL-rename-bound-to-avoid(fmla;L)
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
FOL-bound-rename, 
mFOL-induction, 
uniform-comp-nat-induction, 
mFOL-ext, 
eq_atom: x =a y
, 
any: any x
, 
decidable__l_member, 
list_induction, 
decidable_functionality, 
iff_preserves_decidability, 
nil_member, 
so_lambda: so_lambda4, 
so_apply: x[s1;s2;s3;s4]
, 
uimplies: b supposing a
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
cons_member, 
decidable__or, 
ifthenelse: if b then t else f fi 
, 
null: null(as)
, 
implies: P 
⇒ Q
, 
subtype_rel: A ⊆r B
, 
sq_exists: ∃x:A [B[x]]
, 
so_apply: x[s]
, 
so_lambda: λ2x.t[x]
, 
and: P ∧ Q
, 
prop: ℙ
Lemmas referenced : 
list_wf, 
lifting-strict-spread, 
strict4-apply, 
FOL-bound-rename, 
sq_exists_subtype_rel, 
mFOL-boundvars_wf, 
l_disjoint_wf, 
FOL-abstract_wf, 
AbstractFOFormula+_wf, 
equal_wf, 
length_wf, 
int_subtype_base, 
list_subtype_base, 
mFOL-freevars_wf, 
equal-wf-base, 
mFOL_wf, 
mFOL-induction, 
uniform-comp-nat-induction, 
mFOL-ext, 
decidable__l_member, 
list_induction, 
decidable_functionality, 
iff_preserves_decidability, 
nil_member, 
cons_member, 
decidable__or
Rules used in proof : 
because_Cache, 
intEquality, 
thin, 
isectElimination, 
extract_by_obid, 
introduction, 
universeIsType, 
hypothesis, 
sqequalHypSubstitution, 
sqequalRule, 
cut, 
lambdaFormation_alt, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution, 
baseClosed, 
Error :memTop, 
independent_isectElimination, 
independent_functionElimination, 
dependent_functionElimination, 
equalitySymmetry, 
equalityTransitivity, 
hypothesisEquality, 
equalityIstype, 
inhabitedIsType, 
instantiate, 
applyEquality, 
sqequalBase, 
productIsType, 
closedConclusion, 
applyLambdaEquality, 
productEquality, 
lambdaEquality_alt, 
cumulativity
Latex:
\mforall{}fmla:mFOL().  \mforall{}L:\mBbbZ{}  List.
    (FOL-rename-bound-to-avoid(fmla;L)  \mmember{}  \{fmla':mFOL()| 
                                                                                (mFOL-freevars(fmla')  =  mFOL-freevars(fmla))
                                                                                \mwedge{}  (FOL-abstract(fmla')  =  FOL-abstract(fmla))
                                                                                \mwedge{}  l\_disjoint(\mBbbZ{};L;mFOL-boundvars(fmla'))\}  )
Date html generated:
2020_05_20-AM-09_08_40
Last ObjectModification:
2020_01_24-PM-07_17_32
Theory : minimal-first-order-logic
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