Nuprl Lemma : rat-sub-interval_wf
∀[I,J:ℚInterval]. (rat-sub-interval(I;J) ∈ ℙ)
Proof
Definitions occuring in Statement :
rat-sub-interval: rat-sub-interval(I;J),
rational-interval: ℚInterval,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rat-sub-interval: rat-sub-interval(I;J),
rational-interval: ℚInterval,
prop: ℙ,
and: P ∧ Q
Lemmas referenced :
qle_wf,
rational-interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
spreadEquality,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
hypothesisEquality,
productEquality,
extract_by_obid,
isectElimination,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[I,J:\mBbbQ{}Interval]. (rat-sub-interval(I;J) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-09_17_26
Last ObjectModification:
2019_11_14-PM-08_02_08
Theory : rationals
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