Nuprl Lemma : bounded-above_wf
∀[A:Set(ℝ)]. (bounded-above(A) ∈ ℙ)
Proof
Definitions occuring in Statement :
bounded-above: bounded-above(A),
rset: Set(ℝ),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
bounded-above: bounded-above(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
exists_wf,
real_wf,
upper-bound_wf,
rset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[A:Set(\mBbbR{})]. (bounded-above(A) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-08_09_45
Last ObjectModification:
2015_12_28-AM-01_16_08
Theory : reals
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