Nuprl Lemma : colength_wf_list
∀[T:Type]. ∀[L:T List]. (colength(L) ∈ ℕ)
Proof
Definitions occuring in Statement :
list: T List,
colength: colength(L),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
list: T List,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
termination,
nat_wf,
set-value-type,
le_wf,
int-value-type,
colength_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
isectElimination,
hypothesis,
independent_isectElimination,
sqequalRule,
intEquality,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. (colength(L) \mmember{} \mBbbN{})
Date html generated:
2016_05_14-AM-06_25_41
Last ObjectModification:
2015_12_26-PM-00_42_24
Theory : list_0
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