Nuprl Lemma : length-wf-co-list-islist
∀[T:Type]. ∀[t:co-list-islist(T)]. (||t|| ∈ ℕ)
Proof
Definitions occuring in Statement :
co-list-islist: co-list-islist(T),
length: ||as||,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
co-list-islist: co-list-islist(T),
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
uiff: uiff(P;Q),
and: P ∧ Q
Lemmas referenced :
co-list-islist_wf,
termination,
nat_wf,
set-value-type,
le_wf,
int-value-type,
length-is-colength,
colength_wf,
islist-iff-length-has-value
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
hypothesisEquality,
isect_memberEquality,
because_Cache,
universeEquality,
independent_isectElimination,
intEquality,
lambdaEquality,
natural_numberEquality,
voidElimination,
voidEquality,
productElimination
Latex:
\mforall{}[T:Type]. \mforall{}[t:co-list-islist(T)]. (||t|| \mmember{} \mBbbN{})
Date html generated:
2016_05_15-PM-10_10_51
Last ObjectModification:
2015_12_27-PM-05_58_34
Theory : eval!all
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