Nuprl Lemma : mFOL-freevars-connect-left-contained
∀fmla:mFOL(). mFOL-freevars(mFOconnect-left(fmla)) ⊆ mFOL-freevars(fmla) supposing ↑mFOconnect?(fmla)
Proof
Definitions occuring in Statement :
mFOL-freevars: mFOL-freevars(fmla),
mFOconnect-left: mFOconnect-left(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-left: mFOconnect-left(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-left_wf,
mFOL_wf,
false_wf,
list_wf,
val-union-l-union,
int-deq_wf,
int-valueall-type,
union-contains,
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-left(fmla)) \msubseteq{} mFOL-freevars(fmla) supposing \muparrow{}mFOconnect?(fmla)
Date html generated:
2016_05_15-PM-10_14_40
Last ObjectModification:
2015_12_27-PM-06_32_22
Theory : minimal-first-order-logic
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