Nuprl Lemma : mFOL-freevars-connect-contained
∀x,y:mFOL(). ∀knd:Atom. ∀vs:ℤ List.
  ((mFOL-freevars(x) ⊆ vs ∧ mFOL-freevars(y) ⊆ vs) 
⇒ mFOL-freevars(mFOconnect(knd;x;y)) ⊆ vs)
Proof
Definitions occuring in Statement : 
mFOL-freevars: mFOL-freevars(fmla)
, 
mFOconnect: mFOconnect(knd;left;right)
, 
mFOL: mFOL()
, 
l_contains: A ⊆ B
, 
list: T List
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
and: P ∧ Q
, 
int: ℤ
, 
atom: Atom
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
and: P ∧ Q
, 
mFOL-freevars: mFOL-freevars(fmla)
, 
mFOconnect: mFOconnect(knd;left;right)
, 
mFOL_ind: mFOL_ind, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
prop: ℙ
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
cand: A c∧ B
Lemmas referenced : 
val-union-l-union, 
int-deq_wf, 
mFOL-freevars_wf, 
int-valueall-type, 
and_wf, 
l_contains_wf, 
list_wf, 
mFOL_wf, 
l-union-contained
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
sqequalHypSubstitution, 
productElimination, 
thin, 
sqequalRule, 
cut, 
lemma_by_obid, 
isectElimination, 
intEquality, 
hypothesis, 
hypothesisEquality, 
independent_isectElimination, 
atomEquality, 
dependent_functionElimination, 
independent_functionElimination, 
independent_pairFormation
Latex:
\mforall{}x,y:mFOL().  \mforall{}knd:Atom.  \mforall{}vs:\mBbbZ{}  List.
    ((mFOL-freevars(x)  \msubseteq{}  vs  \mwedge{}  mFOL-freevars(y)  \msubseteq{}  vs)  {}\mRightarrow{}  mFOL-freevars(mFOconnect(knd;x;y))  \msubseteq{}  vs)
Date html generated:
2016_05_15-PM-10_14_45
Last ObjectModification:
2015_12_27-PM-06_32_17
Theory : minimal-first-order-logic
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