Nuprl Lemma : list_wf
∀[T:Type]. (T List ∈ Type)
Proof
Definitions occuring in Statement :
list: T List,
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],
prop: ℙ
Lemmas referenced :
colist_wf,
has-value_wf-partial,
nat_wf,
set-value-type,
le_wf,
int-value-type,
colength_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
setEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
independent_isectElimination,
intEquality,
lambdaEquality,
natural_numberEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. (T List \mmember{} Type)
Date html generated:
2016_05_14-AM-06_25_32
Last ObjectModification:
2015_12_26-PM-00_42_27
Theory : list_0
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