Nuprl Lemma : mtb-seq_wf
∀[X:Type]. ∀[d:metric(X)]. ∀[mtb:m-TB(X;d)]. ∀[s:mtb-cantor(mtb)]. (mtb-seq(mtb;s) ∈ ℕ ⟶ X)
Proof
Definitions occuring in Statement :
mtb-seq: mtb-seq(mtb;s),
mtb-cantor: mtb-cantor(mtb),
m-TB: m-TB(X;d),
metric: metric(X),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
m-TB: m-TB(X;d),
mtb-cantor: mtb-cantor(mtb),
pi1: fst(t),
mtb-seq: mtb-seq(mtb;s),
spreadn: spread3
Lemmas referenced :
istype-nat,
mtb-cantor_wf,
m-TB_wf,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
lambdaEquality_alt,
applyEquality,
hypothesisEquality,
introduction,
extract_by_obid,
hypothesis,
universeIsType,
isectElimination,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[mtb:m-TB(X;d)]. \mforall{}[s:mtb-cantor(mtb)]. (mtb-seq(mtb;s) \mmember{} \mBbbN{} {}\mrightarrow{} X)
Date html generated:
2019_10_30-AM-06_56_27
Last ObjectModification:
2019_10_02-PM-02_30_56
Theory : reals
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