Nuprl Lemma : mtb-cantor_wf
∀[X:Type]. ∀[d:metric(X)]. ∀[mtb:m-TB(X;d)]. (mtb-cantor(mtb) ∈ Type)
Proof
Definitions occuring in Statement :
mtb-cantor: mtb-cantor(mtb),
m-TB: m-TB(X;d),
metric: metric(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mtb-cantor: mtb-cantor(mtb),
m-TB: m-TB(X;d),
top: Top,
subtype_rel: A ⊆r B,
nat_plus: ℕ+
Lemmas referenced :
nat_wf,
int_seg_wf,
pi1_wf_top,
nat_plus_wf,
istype-void,
m-TB_wf,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
closedConclusion,
natural_numberEquality,
setElimination,
rename,
applyEquality,
productElimination,
independent_pairEquality,
hypothesisEquality,
isect_memberEquality_alt,
voidElimination,
lambdaEquality_alt,
universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[mtb:m-TB(X;d)]. (mtb-cantor(mtb) \mmember{} Type)
Date html generated:
2019_10_30-AM-06_55_46
Last ObjectModification:
2019_10_02-PM-02_22_17
Theory : reals
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