Nuprl Lemma : bounded-below_wf
∀[A:Set(ℝ)]. (bounded-below(A) ∈ ℙ)
Proof
Definitions occuring in Statement :
bounded-below: bounded-below(A),
rset: Set(ℝ),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
bounded-below: bounded-below(A)
Lemmas referenced :
rset_wf,
lower-bound_wf,
real_wf,
exists_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesisEquality,
lambdaEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[A:Set(\mBbbR{})]. (bounded-below(A) \mmember{} \mBbbP{})
Date html generated:
2016_11_08-AM-09_06_47
Last ObjectModification:
2016_11_07-PM-02_21_51
Theory : reals
Home
Index