Nuprl Lemma : i-member_wf
∀[I:Interval]. ∀[x:ℝ]. (x ∈ I ∈ ℙ)
Proof
Definitions occuring in Statement :
i-member: r ∈ I,
interval: Interval,
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
i-member: r ∈ I,
interval: Interval,
prop: ℙ,
and: P ∧ Q
Lemmas referenced :
rleq_wf,
rless_wf,
true_wf,
real_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
unionElimination,
productEquality,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I:Interval]. \mforall{}[x:\mBbbR{}]. (x \mmember{} I \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-08_19_14
Last ObjectModification:
2015_12_27-PM-11_57_48
Theory : reals
Home
Index