Nuprl Lemma : apply_alist-eager-map-atom
∀[T:Type]. ∀[L:T List]. ∀[g:T ⟶ Atom]. ∀[f:Top]. ∀[i:{i:Atom| (i ∈ eager-map(g;L))} ].
(apply_alist(AtomDeq;eager-map(λa.<g a, f (g a)>;L);i) ~ f i)
Proof
Definitions occuring in Statement :
apply_alist: apply_alist(eq;L;x),
l_member: (x ∈ l),
eager-map: eager-map(f;as),
list: T List,
atom-deq: AtomDeq,
uall: ∀[x:A]. B[x],
top: Top,
set: {x:A| B[x]} ,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
pair: <a, b>,
atom: Atom,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ
Lemmas referenced :
apply_alist-eager-map2,
atom-value-type,
atom_subtype_base,
atom-deq_wf,
istype-atom,
l_member_wf,
eager-map_wf,
istype-top,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
atomEquality,
independent_isectElimination,
hypothesis,
independent_pairFormation,
axiomSqEquality,
Error :setIsType,
Error :universeIsType,
closedConclusion,
sqequalRule,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
Error :functionIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[g:T {}\mrightarrow{} Atom]. \mforall{}[f:Top]. \mforall{}[i:\{i:Atom| (i \mmember{} eager-map(g;L))\} ].
(apply\_alist(AtomDeq;eager-map(\mlambda{}a.<g a, f (g a)>L);i) \msim{} f i)
Date html generated:
2019_06_20-PM-00_42_59
Last ObjectModification:
2019_02_28-PM-01_49_42
Theory : list_0
Home
Index