Nuprl Lemma : i-finite-subinterval
∀I,J:Interval. (I ⊆ J ⇒ i-finite(J) ⇒ i-finite(I))
Proof
Definitions occuring in Statement :
subinterval: I ⊆ J ,
i-finite: i-finite(I),
interval: Interval,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
rbetween: x≤y≤z,
and: P ∧ Q,
rleq: x ≤ y,
rnonneg: rnonneg(x),
le: A ≤ B,
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
real: ℝ,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
guard: {T},
subinterval: I ⊆ J
Lemmas referenced :
less_than'_wf,
rsub_wf,
real_wf,
nat_plus_wf,
i-member_wf,
uall_wf,
isect_wf,
rbetween_wf,
exists_wf,
subinterval_wf,
interval_wf,
i-finite-iff-bounded,
i-finite_wf,
all_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
hypothesisEquality,
because_Cache,
isect_memberFormation,
introduction,
sqequalRule,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
extract_by_obid,
isectElimination,
applyEquality,
hypothesis,
setElimination,
rename,
minusEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination,
addLevel,
allFunctionality,
impliesFunctionality,
independent_functionElimination,
functionEquality,
independent_isectElimination
Latex:
\mforall{}I,J:Interval. (I \msubseteq{} J {}\mRightarrow{} i-finite(J) {}\mRightarrow{} i-finite(I))
Date html generated:
2016_10_26-AM-09_31_06
Last ObjectModification:
2016_08_22-PM-10_01_38
Theory : reals
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