Nuprl Lemma : is-half-interval_wf
∀[I,J:ℚInterval]. (is-half-interval(I;J) ∈ 𝔹)
Proof
Definitions occuring in Statement :
is-half-interval: is-half-interval(I;J),
rational-interval: ℚInterval,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
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),
uimplies: b supposing a,
or: P ∨ Q,
all: ∀x:A. B[x],
rational-interval: ℚInterval,
is-half-interval: is-half-interval(I;J),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rational-interval_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
Rules used in proof :
universeIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
inhabitedIsType,
axiomEquality,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
independent_isectElimination,
cumulativity,
instantiate,
unionElimination,
dependent_functionElimination,
hypothesis,
isectElimination,
extract_by_obid,
hypothesisEquality,
independent_pairEquality,
thin,
productElimination,
sqequalHypSubstitution,
spreadEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[I,J:\mBbbQ{}Interval]. (is-half-interval(I;J) \mmember{} \mBbbB{})
Date html generated:
2019_10_29-AM-07_50_34
Last ObjectModification:
2019_10_21-PM-00_49_30
Theory : rationals
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