Nuprl Lemma : mFOL-sequent-freevars-contains-concl
∀s:mFOL-sequent(). ∀L:ℤ List.  (L ⊆ mFOL-freevars(snd(s)) 
⇒ L ⊆ mFOL-sequent-freevars(s))
Proof
Definitions occuring in Statement : 
mFOL-sequent-freevars: mFOL-sequent-freevars(s)
, 
mFOL-sequent: mFOL-sequent()
, 
mFOL-freevars: mFOL-freevars(fmla)
, 
l_contains: A ⊆ B
, 
list: T List
, 
pi2: snd(t)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
int: ℤ
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
mFOL-sequent: mFOL-sequent()
, 
mFOL-sequent-freevars: mFOL-sequent-freevars(s)
, 
pi2: snd(t)
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
prop: ℙ
, 
so_apply: x[s]
, 
top: Top
, 
guard: {T}
Lemmas referenced : 
mFOL-freevars_wf, 
list_wf, 
list_induction, 
mFOL_wf, 
all_wf, 
l_contains_wf, 
reduce_wf, 
l-union_wf, 
int-deq_wf, 
reduce_nil_lemma, 
reduce_cons_lemma, 
l-union-right-contains, 
equal_wf, 
mFOL-sequent_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
sqequalHypSubstitution, 
productElimination, 
thin, 
sqequalRule, 
cut, 
introduction, 
extract_by_obid, 
isectElimination, 
hypothesisEquality, 
hypothesis, 
intEquality, 
lambdaEquality, 
functionEquality, 
independent_functionElimination, 
dependent_functionElimination, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
rename, 
because_Cache, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mforall{}s:mFOL-sequent().  \mforall{}L:\mBbbZ{}  List.    (L  \msubseteq{}  mFOL-freevars(snd(s))  {}\mRightarrow{}  L  \msubseteq{}  mFOL-sequent-freevars(s))
Date html generated:
2018_05_21-PM-10_29_33
Last ObjectModification:
2017_07_26-PM-06_41_42
Theory : minimal-first-order-logic
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