Nuprl Lemma : co-list-cons_wf
∀[T:Type]. ∀[h:T]. ∀[t:colist(T)]. (co-list-cons(h;t) ∈ colist(T))
Proof
Definitions occuring in Statement :
co-list-cons: co-list-cons(h;t),
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-list-cons: co-list-cons(h;t),
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
and: P ∧ Q
Lemmas referenced :
subtype_rel_b-union-right,
unit_wf2,
colist_wf,
istype-universe,
colist-ext
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
independent_pairEquality,
hypothesisEquality,
hypothesis,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality,
productElimination
Latex:
\mforall{}[T:Type]. \mforall{}[h:T]. \mforall{}[t:colist(T)]. (co-list-cons(h;t) \mmember{} colist(T))
Date html generated:
2019_10_16-AM-11_38_14
Last ObjectModification:
2019_06_26-PM-04_07_04
Theory : eval!all
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