Nuprl Lemma : rat-interval-third_wf
∀[p:ℝ]. ∀[I:ℚInterval].  (rat-interval-third(p;I) ∈ ℙ)
Proof
Definitions occuring in Statement : 
rat-interval-third: rat-interval-third(p;I)
, 
real: ℝ
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
rational-interval: ℚInterval
Definitions unfolded in proof : 
true: True
, 
less_than': less_than'(a;b)
, 
squash: ↓T
, 
less_than: a < b
, 
rev_implies: P 
⇐ Q
, 
iff: P 
⇐⇒ Q
, 
or: P ∨ Q
, 
guard: {T}
, 
rneq: x ≠ y
, 
uimplies: b supposing a
, 
and: P ∧ Q
, 
prop: ℙ
, 
implies: P 
⇒ Q
, 
rational-interval: ℚInterval
, 
top: Top
, 
all: ∀x:A. B[x]
, 
rat-interval-third: rat-interval-third(p;I)
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
real_wf, 
rational-interval_wf, 
rless_wf, 
rless-int, 
int-to-real_wf, 
rmul_wf, 
radd_wf, 
rdiv_wf, 
req_wf, 
or_wf, 
rat2real_wf, 
rleq_wf, 
istype-void, 
member_rccint_lemma
Rules used in proof : 
inhabitedIsType, 
isectIsTypeImplies, 
equalitySymmetry, 
equalityTransitivity, 
axiomEquality, 
universeIsType, 
baseClosed, 
imageMemberEquality, 
independent_pairFormation, 
independent_functionElimination, 
inrFormation_alt, 
independent_isectElimination, 
natural_numberEquality, 
closedConclusion, 
because_Cache, 
hypothesisEquality, 
isectElimination, 
productEquality, 
functionEquality, 
productElimination, 
hypothesis, 
voidElimination, 
isect_memberEquality_alt, 
thin, 
dependent_functionElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
sqequalRule, 
cut, 
introduction, 
isect_memberFormation_alt, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}[p:\mBbbR{}].  \mforall{}[I:\mBbbQ{}Interval].    (rat-interval-third(p;I)  \mmember{}  \mBbbP{})
Date html generated:
2019_10_31-AM-06_03_40
Last ObjectModification:
2019_10_30-PM-01_29_44
Theory : real!vectors
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