Nuprl Lemma : partition-refines_transitivity
∀I:Interval. ∀P,Q,R:partition(I). (P refines Q ⇒ Q refines R ⇒ P refines R) supposing icompact(I)
Proof
Definitions occuring in Statement :
partition-refines: P refines Q,
partition: partition(I),
icompact: icompact(I),
interval: Interval,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
partition-refines: P refines Q,
all: ∀x:A. B[x],
uimplies: b supposing a,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
partition: partition(I),
prop: ℙ
Lemmas referenced :
frs-refines_transitivity,
frs-refines_wf,
partition_wf,
icompact_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
independent_functionElimination,
hypothesis,
independent_isectElimination
Latex:
\mforall{}I:Interval. \mforall{}P,Q,R:partition(I). (P refines Q {}\mRightarrow{} Q refines R {}\mRightarrow{} P refines R) supposing icompact(I)
Date html generated:
2016_05_18-AM-09_05_51
Last ObjectModification:
2015_12_27-PM-11_31_58
Theory : reals
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