Nuprl Lemma : subinterval-trivial
∀I:Interval. I ⊆ [left-endpoint(I), right-endpoint(I)] supposing icompact(I)
Proof
Definitions occuring in Statement :
subinterval: I ⊆ J ,
icompact: icompact(I),
rccint: [l, u],
right-endpoint: right-endpoint(I),
left-endpoint: left-endpoint(I),
interval: Interval,
uimplies: b supposing a,
all: ∀x:A. B[x]
Definitions unfolded in proof :
false: False,
cand: A c∧ B,
and: P ∧ Q,
bfalse: ff,
bor: p ∨bq,
assert: ↑b,
btrue: tt,
ifthenelse: if b then t else f fi ,
bnot: ¬bb,
isl: isl(x),
i-closed: i-closed(I),
i-finite: i-finite(I),
i-member: r ∈ I,
pi2: snd(t),
pi1: fst(t),
outl: outl(x),
endpoints: endpoints(I),
top: Top,
left-endpoint: left-endpoint(I),
right-endpoint: right-endpoint(I),
icompact: icompact(I),
interval: Interval,
subinterval: I ⊆ J ,
uall: ∀[x:A]. B[x],
prop: ℙ,
squash: ↓T,
implies: P ⇒ Q,
sq_stable: SqStable(P),
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
real_wf,
i-member_wf,
member_rccint_lemma,
interval_wf,
icompact_wf,
sq_stable__icompact
Rules used in proof :
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
unionElimination,
productElimination,
isectElimination,
imageElimination,
baseClosed,
imageMemberEquality,
sqequalRule,
independent_functionElimination,
hypothesis,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}I:Interval. I \msubseteq{} [left-endpoint(I), right-endpoint(I)] supposing icompact(I)
Date html generated:
2018_07_29-AM-09_40_17
Last ObjectModification:
2018_07_02-PM-02_25_40
Theory : reals
Home
Index