Nuprl Lemma : totally-bounded_wf
∀[A:Set(ℝ)]. (totally-bounded(A) ∈ ℙ)
Proof
Definitions occuring in Statement :
totally-bounded: totally-bounded(A),
rset: Set(ℝ),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
totally-bounded: totally-bounded(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
nat_plus: ℕ+,
and: P ∧ Q,
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x]
Lemmas referenced :
all_wf,
real_wf,
rless_wf,
int-to-real_wf,
exists_wf,
nat_plus_wf,
int_seg_wf,
rset-member_wf,
rabs_wf,
rsub_wf,
rset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
functionEquality,
natural_numberEquality,
hypothesisEquality,
because_Cache,
setElimination,
rename,
productEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[A:Set(\mBbbR{})]. (totally-bounded(A) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-08_14_44
Last ObjectModification:
2015_12_28-AM-01_17_16
Theory : reals
Home
Index