Nuprl Lemma : length-in-prop-if-co-list
∀[T:Type]. ∀[t:colist(T)]. (∃n:ℕ. (||t|| = n ∈ partial(ℤ)) ∈ ℙ)
Proof
Definitions occuring in Statement :
length: ||as||,
colist: colist(T),
partial: partial(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
exists: ∃x:A. B[x],
member: t ∈ T,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
exists_wf,
nat_wf,
equal_wf,
partial_wf,
length-in-bar-int-if-co-list,
subtype_rel_set,
le_wf,
istype-int,
inclusion-partial,
int-value-type,
colist_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
lambdaEquality_alt,
intEquality,
hypothesisEquality,
applyEquality,
because_Cache,
natural_numberEquality,
independent_isectElimination,
universeIsType,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[t:colist(T)]. (\mexists{}n:\mBbbN{}. (||t|| = n) \mmember{} \mBbbP{})
Date html generated:
2019_10_16-AM-11_38_19
Last ObjectModification:
2018_10_11-PM-03_19_39
Theory : eval!all
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