### Nuprl Lemma : eager-map_wf

[A,B:Type].  ∀[f:A ⟶ B]. ∀[l:A List].  (eager-map(f;l) ∈ List) supposing value-type(B)

Proof

Definitions occuring in Statement :  eager-map: eager-map(f;as) list: List value-type: value-type(T) uimplies: supposing a uall: [x:A]. B[x] member: t ∈ T function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a eager-map: eager-map(f;as) all: x:A. B[x] nat: implies:  Q false: False ge: i ≥  guard: {T} prop: subtype_rel: A ⊆B or: P ∨ Q so_lambda: so_lambda(x,y,z.t[x; y; z]) top: Top so_apply: x[s1;s2;s3] cons: [a b] colength: colength(L) so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] squash: T sq_stable: SqStable(P) uiff: uiff(P;Q) and: P ∧ Q le: A ≤ B not: ¬A less_than': less_than'(a;b) true: True decidable: Dec(P) iff: ⇐⇒ Q rev_implies:  Q subtract: m nil: [] it: so_lambda: λ2x.t[x] so_apply: x[s] sq_type: SQType(T) less_than: a < b has-value: (a)↓
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination natural_numberEquality independent_isectElimination independent_functionElimination voidElimination lambdaEquality dependent_functionElimination axiomEquality equalityTransitivity equalitySymmetry cumulativity applyEquality because_Cache unionElimination isect_memberEquality voidEquality promote_hyp hypothesis_subsumption productElimination applyLambdaEquality imageMemberEquality baseClosed imageElimination addEquality dependent_set_memberEquality independent_pairFormation minusEquality intEquality instantiate callbyvalueReduce functionExtensionality functionEquality universeEquality

Latex:
\mforall{}[A,B:Type].    \mforall{}[f:A  {}\mrightarrow{}  B].  \mforall{}[l:A  List].    (eager-map(f;l)  \mmember{}  B  List)  supposing  value-type(B)

Date html generated: 2017_04_14-AM-08_34_21
Last ObjectModification: 2017_02_27-PM-03_22_12

Theory : list_0

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