Nuprl Lemma : co-list-islist-islist
∀[T:Type]. ∀[t:co-list-islist(T)]. islist(t)
Proof
Definitions occuring in Statement :
co-list-islist: co-list-islist(T),
islist: islist(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,
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
islist: islist(t),
has-value: (a)↓
Lemmas referenced :
co-list-islist-ext-list,
subtype_rel_weakening,
co-list-islist_wf,
list_wf,
islist-list,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
cumulativity,
independent_isectElimination,
sqequalRule,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomSqleEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[t:co-list-islist(T)]. islist(t)
Date html generated:
2018_05_21-PM-10_20_21
Last ObjectModification:
2017_07_26-PM-06_37_24
Theory : eval!all
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