Nuprl Lemma : co-list-islist-ext-list
∀[T:Type]. co-list-islist(T) ≡ T List
Proof
Definitions occuring in Statement :
co-list-islist: co-list-islist(T),
list: T List,
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
co-list-islist: co-list-islist(T),
list: T List,
uiff: uiff(P;Q),
uimplies: b supposing a,
top: Top,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
rev_uimplies: rev_uimplies(P;Q),
bool: 𝔹
Lemmas referenced :
islist-iff-length-has-value,
length-is-colength,
has-value_wf-partial,
nat_wf,
set-value-type,
le_wf,
int-value-type,
colength_wf,
co-list-islist_wf,
bool_wf,
union-value-type,
unit_wf2,
is-list_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
hypothesisEquality,
extract_by_obid,
isectElimination,
hypothesis,
productElimination,
independent_isectElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
intEquality,
natural_numberEquality,
cumulativity,
because_Cache,
independent_pairEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. co-list-islist(T) \mequiv{} T List
Date html generated:
2018_05_21-PM-10_20_19
Last ObjectModification:
2017_07_26-PM-06_37_22
Theory : eval!all
Home
Index