### Nuprl Lemma : eager-map-is-map

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

Proof

Definitions occuring in Statement :  eager-map: `eager-map(f;as)` map: `map(f;as)` list: `T List` value-type: `value-type(T)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` function: `x:A ⟶ B[x]` universe: `Type` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` eager-map: `eager-map(f;as)` all: `∀x:A. B[x]` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` guard: `{T}` prop: `ℙ` subtype_rel: `A ⊆r 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: `λ2x y.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: `P `⇐⇒` Q` rev_implies: `P `` Q` subtract: `n - 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 intWeakElimination natural_numberEquality independent_isectElimination independent_functionElimination voidElimination sqequalRule lambdaEquality dependent_functionElimination sqequalAxiom cumulativity applyEquality because_Cache unionElimination isect_memberEquality voidEquality promote_hyp hypothesis_subsumption productElimination applyLambdaEquality imageMemberEquality baseClosed imageElimination addEquality dependent_set_memberEquality independent_pairFormation minusEquality equalityTransitivity equalitySymmetry intEquality instantiate callbyvalueReduce functionExtensionality functionEquality universeEquality

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

Date html generated: 2017_04_14-AM-08_34_42
Last ObjectModification: 2017_02_27-PM-03_22_29

Theory : list_0

Home Index