Nuprl Lemma : sup_wf
∀[A:Set(ℝ)]. ∀[b:ℝ]. (sup(A) = b ∈ ℙ)
Proof
Definitions occuring in Statement :
sup: sup(A) = b,
rset: Set(ℝ),
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
sup: sup(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 :
and_wf,
upper-bound_wf,
all_wf,
real_wf,
rless_wf,
int-to-real_wf,
exists_wf,
rset-member_wf,
rsub_wf,
rset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
functionEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:Set(\mBbbR{})]. \mforall{}[b:\mBbbR{}]. (sup(A) = b \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-08_10_09
Last ObjectModification:
2015_12_28-AM-01_15_59
Theory : reals
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