### Nuprl Lemma : mapc_wf

`∀[A,B:Type]. ∀[f:A ⟶ B].  (mapc(f) ∈ (A List) ⟶ (B List))`

Proof

Definitions occuring in Statement :  mapc: `mapc(f)` list: `T List` 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` all: `∀x:A. B[x]` subtype_rel: `A ⊆r B` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` guard: `{T}` uimplies: `b supposing a` prop: `ℙ` or: `P ∨ Q` mapc: `mapc(f)` 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`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution hypothesis sqequalRule axiomEquality equalityTransitivity equalitySymmetry functionEquality cumulativity hypothesisEquality isect_memberEquality isectElimination thin because_Cache universeEquality lambdaFormation extract_by_obid functionExtensionality dependent_functionElimination voidElimination applyEquality instantiate setElimination rename intWeakElimination natural_numberEquality independent_isectElimination independent_functionElimination lambdaEquality unionElimination voidEquality promote_hyp hypothesis_subsumption productElimination applyLambdaEquality imageMemberEquality baseClosed imageElimination addEquality dependent_set_memberEquality independent_pairFormation minusEquality intEquality

Latex:
\mforall{}[A,B:Type].  \mforall{}[f:A  {}\mrightarrow{}  B].    (mapc(f)  \mmember{}  (A  List)  {}\mrightarrow{}  (B  List))

Date html generated: 2017_04_14-AM-08_34_32
Last ObjectModification: 2017_02_27-PM-03_22_10

Theory : list_0

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