Nuprl Lemma : mFOL-freevars-connect-right-contained
∀fmla:mFOL(). mFOL-freevars(mFOconnect-right(fmla)) ⊆ mFOL-freevars(fmla) supposing ↑mFOconnect?(fmla)
Proof
Definitions occuring in Statement : 
mFOL-freevars: mFOL-freevars(fmla)
, 
mFOconnect-right: mFOconnect-right(v)
, 
mFOconnect?: mFOconnect?(v)
, 
mFOL: mFOL()
, 
l_contains: A ⊆ B
, 
assert: ↑b
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
, 
int: ℤ
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
prop: ℙ
, 
so_apply: x[s]
, 
implies: P 
⇒ Q
, 
mFOatomic: name(vars)
, 
mFOconnect?: mFOconnect?(v)
, 
pi1: fst(t)
, 
mFOconnect-right: mFOconnect-right(v)
, 
pi2: snd(t)
, 
eq_atom: x =a y
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
all: ∀x:A. B[x]
, 
false: False
, 
mFOconnect: mFOconnect(knd;left;right)
, 
btrue: tt
, 
true: True
, 
mFOL-freevars: mFOL-freevars(fmla)
, 
mFOL_ind: mFOL_ind, 
mFOquant: mFOquant(isall;var;body)
, 
guard: {T}
Lemmas referenced : 
mFOL-induction, 
isect_wf, 
assert_wf, 
mFOconnect?_wf, 
l_contains_wf, 
mFOL-freevars_wf, 
mFOconnect-right_wf, 
mFOL_wf, 
false_wf, 
list_wf, 
val-union-l-union, 
int-deq_wf, 
int-valueall-type, 
union-contains2, 
true_wf, 
bool_wf
Rules used in proof : 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isectElimination, 
thin, 
sqequalRule, 
lambdaEquality, 
hypothesisEquality, 
hypothesis, 
intEquality, 
independent_isectElimination, 
independent_functionElimination, 
lambdaFormation, 
isect_memberFormation, 
introduction, 
voidElimination, 
rename, 
atomEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
because_Cache
Latex:
\mforall{}fmla:mFOL()
    mFOL-freevars(mFOconnect-right(fmla))  \msubseteq{}  mFOL-freevars(fmla)  supposing  \muparrow{}mFOconnect?(fmla)
Date html generated:
2016_05_15-PM-10_14_43
Last ObjectModification:
2015_12_27-PM-06_32_18
Theory : minimal-first-order-logic
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