Nuprl Lemma : subinterval_transitivity
∀[I,J,K:Interval]. (I ⊆ J ⇒ J ⊆ K ⇒ I ⊆ K )
Proof
Definitions occuring in Statement :
subinterval: I ⊆ J ,
interval: Interval,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
subinterval: I ⊆ J ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T}
Lemmas referenced :
i-member_wf,
real_wf,
all_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
functionEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[I,J,K:Interval]. (I \msubseteq{} J {}\mRightarrow{} J \msubseteq{} K {}\mRightarrow{} I \msubseteq{} K )
Date html generated:
2016_05_18-AM-08_49_31
Last ObjectModification:
2015_12_27-PM-11_43_38
Theory : reals
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