Nuprl Lemma : list-value-type
∀[T:Type]. value-type(T List)
Proof
Definitions occuring in Statement :
list: T List,
value-type: value-type(T),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
list: T List,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
nat: ℕ,
so_apply: x[s],
value-type: value-type(T),
has-value: (a)↓,
prop: ℙ
Lemmas referenced :
set-value-type,
colist_wf,
has-value_wf-partial,
nat_wf,
le_wf,
int-value-type,
colength_wf,
colist-value-type,
equal-wf-base,
list_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
independent_isectElimination,
intEquality,
natural_numberEquality,
cumulativity,
isect_memberEquality,
axiomSqleEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. value-type(T List)
Date html generated:
2016_05_14-AM-06_25_46
Last ObjectModification:
2015_12_26-PM-00_42_22
Theory : list_0
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