Nuprl Lemma : partition-refines_weakening
∀I:Interval. ∀P,Q:partition(I). ((P = Q ∈ partition(I)) ⇒ P refines Q) 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,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
partition-refines: P refines Q,
partition: partition(I)
Lemmas referenced :
partition-refines_wf,
equal_wf,
partition_wf,
icompact_wf,
interval_wf,
frs-refines_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
hypothesis,
thin,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
hypothesisEquality,
independent_isectElimination,
sqequalRule,
isectElimination,
setElimination,
rename,
because_Cache,
independent_functionElimination
Latex:
\mforall{}I:Interval. \mforall{}P,Q:partition(I). ((P = Q) {}\mRightarrow{} P refines Q) supposing icompact(I)
Date html generated:
2016_10_26-AM-09_41_26
Last ObjectModification:
2016_07_12-AM-08_22_08
Theory : reals
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