Nuprl Lemma : colength_wf
∀[T:Type]. ∀[L:colist(T)]. (colength(L) ∈ partial(ℕ))
Proof
Definitions occuring in Statement :
colength: colength(L),
colist: colist(T),
partial: partial(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
colength: colength(L),
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
colist-fix-ap-partial,
nat_wf,
set-value-type,
le_wf,
istype-int,
int-value-type,
nat-mono,
b-union_wf,
unit_wf2,
istype-universe,
partial_wf,
colist_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
sqequalRule,
intEquality,
Error :lambdaEquality_alt,
natural_numberEquality,
hypothesisEquality,
Error :isect_memberEquality_alt,
because_Cache,
Error :universeIsType,
productEquality,
Error :functionIsType,
Error :inhabitedIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:colist(T)]. (colength(L) \mmember{} partial(\mBbbN{}))
Date html generated:
2019_06_20-PM-00_38_13
Last ObjectModification:
2018_10_06-PM-06_09_18
Theory : list_0
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