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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