Nuprl Lemma : partition-mesh-nonneg
∀[I:Interval]. ∀[p:partition(I)]. (r0 ≤ partition-mesh(I;p)) supposing icompact(I)
Proof
Definitions occuring in Statement :
partition-mesh: partition-mesh(I;p),
partition: partition(I),
icompact: icompact(I),
interval: Interval,
rleq: x ≤ y,
int-to-real: r(n),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
partition-mesh: partition-mesh(I;p),
implies: P ⇒ Q,
rleq: x ≤ y,
rnonneg: rnonneg(x),
all: ∀x:A. B[x],
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
real: ℝ,
prop: ℙ
Lemmas referenced :
frs-mesh-nonneg,
full-partition_wf,
full-partition-non-dec,
less_than'_wf,
rsub_wf,
partition-mesh_wf,
int-to-real_wf,
real_wf,
nat_plus_wf,
partition_wf,
icompact_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
independent_functionElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
productElimination,
independent_pairEquality,
because_Cache,
applyEquality,
natural_numberEquality,
setElimination,
rename,
minusEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination
Latex:
\mforall{}[I:Interval]. \mforall{}[p:partition(I)]. (r0 \mleq{} partition-mesh(I;p)) supposing icompact(I)
Date html generated:
2016_05_18-AM-08_56_48
Last ObjectModification:
2015_12_27-PM-11_37_01
Theory : reals
Home
Index