Nuprl Lemma : list-to-set_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:T List]. (list-to-set(eq;L) ∈ T List)
Proof
Definitions occuring in Statement :
list-to-set: list-to-set(eq;L),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
list-to-set: list-to-set(eq;L)
Lemmas referenced :
l-union_wf,
nil_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[L:T List]. (list-to-set(eq;L) \mmember{} T List)
Date html generated:
2016_05_14-PM-03_25_37
Last ObjectModification:
2015_12_26-PM-06_22_37
Theory : decidable!equality
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