Nuprl Lemma : has-value-is-list-map-iff-has-value-is-list
∀[T:Type]. ∀[t:colist(T)]. ∀[f:Base]. ((is-list(t))↓ ⇐⇒ (is-list(map(f;t)))↓)
Proof
Definitions occuring in Statement :
is-list: is-list(t),
map: map(f;as),
colist: colist(T),
has-value: (a)↓,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
uimplies: b supposing a,
bool: 𝔹,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
has-value: (a)↓
Lemmas referenced :
is-list-map,
has-value_wf-partial,
bool_wf,
union-value-type,
unit_wf2,
is-list_wf,
base_wf,
colist_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
independent_isectElimination,
because_Cache,
cumulativity,
hypothesisEquality,
independent_pairFormation,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
axiomSqleEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[t:colist(T)]. \mforall{}[f:Base]. ((is-list(t))\mdownarrow{} \mLeftarrow{}{}\mRightarrow{} (is-list(map(f;t)))\mdownarrow{})
Date html generated:
2018_05_21-PM-10_19_51
Last ObjectModification:
2017_07_26-PM-06_37_16
Theory : eval!all
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