Nuprl Lemma : i-member-approx
∀I:Interval. ∀x:ℝ. ∀n:ℕ+. ((x ∈ i-approx(I;n)) ⇒ (x ∈ I))
Proof
Definitions occuring in Statement :
i-approx: i-approx(I;n),
i-member: r ∈ I,
interval: Interval,
real: ℝ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
prop: ℙ,
uall: ∀[x:A]. B[x]
Lemmas referenced :
i-member-iff,
i-member_wf,
i-approx_wf,
nat_plus_wf,
real_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
independent_functionElimination,
dependent_pairFormation,
hypothesis,
isectElimination
Latex:
\mforall{}I:Interval. \mforall{}x:\mBbbR{}. \mforall{}n:\mBbbN{}\msupplus{}. ((x \mmember{} i-approx(I;n)) {}\mRightarrow{} (x \mmember{} I))
Date html generated:
2016_05_18-AM-08_40_50
Last ObjectModification:
2015_12_27-PM-11_51_12
Theory : reals
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