Nuprl Lemma : rccint-icompact
∀a,b:ℝ. (a ≤ b ⇐⇒ icompact([a, b]))
Proof
Definitions occuring in Statement :
icompact: icompact(I),
rccint: [l, u],
rleq: x ≤ y,
real: ℝ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
rccint: [l, u],
icompact: icompact(I),
i-finite: i-finite(I),
i-closed: i-closed(I),
i-nonvoid: i-nonvoid(I),
isl: isl(x),
outl: outl(x),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
btrue: tt,
assert: ↑b,
bor: p ∨bq,
bfalse: ff,
i-member: r ∈ I,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
prop: ℙ,
true: True,
rev_implies: P ⇐ Q,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
rleq_weakening_equal,
and_wf,
rleq_wf,
rleq_transitivity,
exists_wf,
real_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
independent_pairFormation,
dependent_pairFormation,
hypothesisEquality,
hypothesis,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
independent_isectElimination,
natural_numberEquality,
productElimination,
lambdaEquality
Latex:
\mforall{}a,b:\mBbbR{}. (a \mleq{} b \mLeftarrow{}{}\mRightarrow{} icompact([a, b]))
Date html generated:
2016_05_18-AM-08_45_38
Last ObjectModification:
2015_12_27-PM-11_50_12
Theory : reals
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