Nuprl Lemma : rat-interval-intersection-idemp
∀[I:ℚInterval]. (I ⋂ I = I ∈ ℚInterval)
Proof
Definitions occuring in Statement :
rat-interval-intersection: I ⋂ J,
rational-interval: ℚInterval,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
member: t ∈ T,
rat-interval-intersection: I ⋂ J,
rational-interval: ℚInterval,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rational-interval_wf,
subtype_rel_self,
qmin-idempotent,
qmax-idempotent
Rules used in proof :
universeIsType,
because_Cache,
applyEquality,
hypothesis,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
independent_pairEquality,
sqequalRule,
thin,
productElimination,
sqequalHypSubstitution,
cut,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[I:\mBbbQ{}Interval]. (I \mcap{} I = I)
Date html generated:
2019_10_29-AM-07_48_32
Last ObjectModification:
2019_10_18-PM-00_57_04
Theory : rationals
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