Nuprl Lemma : rat-interval-intersection_wf
∀[I,J:ℚInterval]. (I ⋂ J ∈ ℚInterval)
Proof
Definitions occuring in Statement :
rat-interval-intersection: I ⋂ J,
rational-interval: ℚInterval,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
rational-interval: ℚInterval,
rat-interval-intersection: I ⋂ J,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rational-interval_wf,
qmin_wf,
qmax_wf
Rules used in proof :
universeIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
inhabitedIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
isectElimination,
extract_by_obid,
hypothesisEquality,
independent_pairEquality,
thin,
productElimination,
sqequalHypSubstitution,
spreadEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[I,J:\mBbbQ{}Interval]. (I \mcap{} J \mmember{} \mBbbQ{}Interval)
Date html generated:
2019_10_29-AM-07_48_20
Last ObjectModification:
2019_10_17-PM-01_24_53
Theory : rationals
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