Nuprl Lemma : rmin-i-member
∀I:Interval. ∀a,b:ℝ. ((a ∈ I) ⇒ (b ∈ I) ⇒ (rmin(a;b) ∈ I))
Proof
Definitions occuring in Statement :
i-member: r ∈ I,
interval: Interval,
rmin: rmin(x;y),
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
interval: Interval,
i-member: r ∈ I,
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
iff: P ⇐⇒ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
or: P ∨ Q,
prop: ℙ,
true: True
Lemmas referenced :
rmin_ub,
rmin_lb,
rleq_wf,
and_wf,
real_wf,
rmin_strict_ub,
rless_wf,
rmin_strict_lb,
true_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
unionElimination,
sqequalRule,
cut,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
because_Cache,
independent_functionElimination,
hypothesis,
independent_pairFormation,
isectElimination,
independent_isectElimination,
inlFormation,
natural_numberEquality
Latex:
\mforall{}I:Interval. \mforall{}a,b:\mBbbR{}. ((a \mmember{} I) {}\mRightarrow{} (b \mmember{} I) {}\mRightarrow{} (rmin(a;b) \mmember{} I))
Date html generated:
2016_05_18-AM-08_47_53
Last ObjectModification:
2015_12_27-PM-11_47_02
Theory : reals
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