Nuprl Lemma : lower-bound_wf
∀[A:Set(ℝ)]. ∀[b:ℝ]. (lower-bound(A;b) ∈ ℙ)
Proof
Definitions occuring in Statement :
lower-bound: lower-bound(A;b),
rset: Set(ℝ),
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
lower-bound: lower-bound(A;b),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
all_wf,
real_wf,
rset-member_wf,
rleq_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,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:Set(\mBbbR{})]. \mforall{}[b:\mBbbR{}]. (lower-bound(A;b) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-08_09_31
Last ObjectModification:
2015_12_28-AM-01_15_49
Theory : reals
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