Nuprl Lemma : half-point-interval
∀[I:ℚInterval]. ∀[a:ℚ]. I = [a] ∈ ℚInterval supposing ↑is-half-interval(I;[a])
Proof
Definitions occuring in Statement :
is-half-interval: is-half-interval(I;J),
rat-point-interval: [a],
rational-interval: ℚInterval,
rationals: ℚ,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
subtype_rel: A ⊆r B,
true: True,
squash: ↓T,
prop: ℙ,
ifthenelse: if b then t else f fi ,
band: p ∧b q,
bfalse: ff,
and: P ∧ Q,
uiff: uiff(P;Q),
guard: {T},
implies: P ⇒ Q,
sq_type: SQType(T),
or: P ∨ Q,
all: ∀x:A. B[x],
rat-point-interval: [a],
is-half-interval: is-half-interval(I;J),
rational-interval: ℚInterval,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
assert_of_band,
assert_of_bor,
iff_weakening_uiff,
iff_transitivity,
iff_weakening_equal,
subtype_rel_self,
qavg-same,
istype-universe,
true_wf,
squash_wf,
equal_wf,
bfalse_wf,
qavg_wf,
assert-qeq,
btrue_wf,
band_wf,
eqtt_to_assert,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases,
qeq_wf2,
bor_wf,
assert_wf,
rational-interval_wf,
rationals_wf,
rat-point-interval_wf,
is-half-interval_wf,
istype-assert
Rules used in proof :
lambdaFormation_alt,
independent_pairEquality,
inrFormation_alt,
baseClosed,
imageMemberEquality,
natural_numberEquality,
universeEquality,
imageElimination,
lambdaEquality_alt,
applyEquality,
promote_hyp,
independent_pairFormation,
inlFormation_alt,
unionIsType,
equalityIstype,
productIsType,
productEquality,
because_Cache,
unionEquality,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
independent_isectElimination,
cumulativity,
instantiate,
unionElimination,
dependent_functionElimination,
universeIsType,
inhabitedIsType,
isectIsTypeImplies,
axiomEquality,
isect_memberEquality_alt,
hypothesisEquality,
isectElimination,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
productElimination,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[I:\mBbbQ{}Interval]. \mforall{}[a:\mBbbQ{}]. I = [a] supposing \muparrow{}is-half-interval(I;[a])
Date html generated:
2019_10_29-AM-07_50_41
Last ObjectModification:
2019_10_23-PM-00_11_47
Theory : rationals
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