Nuprl Lemma : rbetween_wf
∀[x,y,z:ℝ]. (x≤y≤z ∈ ℙ)
Proof
Definitions occuring in Statement :
rbetween: x≤y≤z,
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
rbetween: x≤y≤z,
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
and_wf,
rleq_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[x,y,z:\mBbbR{}]. (x\mleq{}y\mleq{}z \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-07_06_22
Last ObjectModification:
2015_12_28-AM-00_37_09
Theory : reals
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