Nuprl Lemma : nil-sub-co-list
∀[T:Type]. ∀[s:colist(T)]. sub-co-list(T;[];s)
Proof
Definitions occuring in Statement :
sub-co-list: sub-co-list(T;s1;s2),
nil: [],
colist: colist(T),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
list: T List,
sub-co-list: sub-co-list(T;s1;s2),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
nil_wf,
nat_wf,
list-at_wf,
colist_wf,
istype-universe,
list_at_nil2_lemma,
istype-void
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
Error :lambdaEquality_alt,
setElimination,
rename,
hypothesisEquality,
Error :inhabitedIsType,
because_Cache,
sqequalRule,
Error :dependent_pairFormation_alt,
equalityTransitivity,
equalitySymmetry,
Error :equalityIstype,
baseClosed,
sqequalBase,
Error :universeIsType,
instantiate,
universeEquality,
dependent_functionElimination,
Error :isect_memberEquality_alt,
voidElimination
Latex:
\mforall{}[T:Type]. \mforall{}[s:colist(T)]. sub-co-list(T;[];s)
Date html generated:
2019_06_20-PM-01_22_02
Last ObjectModification:
2019_01_02-PM-04_40_26
Theory : list_1
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