Nuprl Lemma : icompact-length-nonneg
∀[I:Interval]. r0 ≤ |I| supposing icompact(I)
Proof
Definitions occuring in Statement :
icompact: icompact(I),
i-length: |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,
icompact: icompact(I),
and: P ∧ Q,
i-length: |I|,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
rleq: x ≤ y,
rnonneg: rnonneg(x),
all: ∀x:A. B[x],
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
prop: ℙ,
rsub: x - y,
i-nonvoid: i-nonvoid(I),
exists: ∃x:A. B[x],
rbetween: x≤y≤z,
guard: {T}
Lemmas referenced :
radd-preserves-rleq,
rsub_wf,
right-endpoint_wf,
left-endpoint_wf,
less_than'_wf,
i-length_wf,
int-to-real_wf,
nat_plus_wf,
icompact_wf,
interval_wf,
rleq_wf,
radd_wf,
rminus_wf,
uiff_transitivity,
rleq_functionality,
radd_comm,
radd_functionality,
req_weakening,
radd-rminus-assoc,
radd-zero-both,
i-member-finite,
rleq_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
lemma_by_obid,
isectElimination,
because_Cache,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
independent_pairEquality,
applyEquality,
natural_numberEquality,
minusEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination,
independent_functionElimination
Latex:
\mforall{}[I:Interval]. r0 \mleq{} |I| supposing icompact(I)
Date html generated:
2016_05_18-AM-08_46_57
Last ObjectModification:
2015_12_27-PM-11_47_38
Theory : reals
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