Nuprl Lemma : co-cons_wf
∀[T:Type]. ∀[x:T]. ∀[L:colist(T)]. ([x / L] ∈ colist(T))
Proof
Definitions occuring in Statement :
co-cons: [x / L],
colist: colist(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
co-cons: [x / L],
subtype_rel: A ⊆r B
Lemmas referenced :
colist_wf,
istype-universe,
product_subtype_colist
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
independent_pairEquality,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
extract_by_obid,
isectElimination,
thin,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[L:colist(T)]. ([x / L] \mmember{} colist(T))
Date html generated:
2019_06_20-PM-00_38_12
Last ObjectModification:
2018_12_04-PM-00_20_06
Theory : list_0
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