Nuprl Lemma : islist-append-nil-is-list
∀[l:Base]. l ∈ Base List supposing islist(l @ [])
Proof
Definitions occuring in Statement :
islist: islist(t),
append: as @ bs,
nil: [],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
top: Top,
prop: ℙ
Lemmas referenced :
base_wf,
islist_wf,
islist-implies-is-list,
islist-append-nil-sqequal-islist
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lemma_by_obid,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
hypothesisEquality,
independent_isectElimination,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
baseApply,
closedConclusion,
baseClosed,
because_Cache
Latex:
\mforall{}[l:Base]. l \mmember{} Base List supposing islist(l @ [])
Date html generated:
2016_05_15-PM-10_07_26
Last ObjectModification:
2016_01_16-PM-04_08_43
Theory : eval!all
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