Nuprl Lemma : subinterval_wf
∀[I,J:Interval]. (I ⊆ J ∈ ℙ)
Proof
Definitions occuring in Statement :
subinterval: I ⊆ J ,
interval: Interval,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
subinterval: I ⊆ J ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
all_wf,
real_wf,
i-member_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
functionEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[I,J:Interval]. (I \msubseteq{} J \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-08_49_21
Last ObjectModification:
2015_12_27-PM-11_44_11
Theory : reals
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