### Nuprl Lemma : list-accum_wf

`∀[T,T':Type]. ∀[l:T List]. ∀[b:T']. ∀[f:(T List) ⟶ T' ⟶ T ⟶ T'].  (list-accum(t,a,h.f[t;a;h];b;l) ∈ T')`

Proof

Definitions occuring in Statement :  list-accum: `list-accum(t,a,h.f[t; a; h];b;L)` list: `T List` uall: `∀[x:A]. B[x]` so_apply: `x[s1;s2;s3]` 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]` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` guard: `{T}` uimplies: `b supposing a` prop: `ℙ` subtype_rel: `A ⊆r B` or: `P ∨ Q` list-accum: `list-accum(t,a,h.f[t; a; h];b;L)` nil: `[]` it: `⋅` cons: `[a / b]` colength: `colength(L)` so_lambda: `λ2x y.t[x; y]` top: `Top` 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` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_type: `SQType(T)` less_than: `a < b` so_apply: `x[s1;s2;s3]`
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 isect_memberEquality axiomEquality equalityTransitivity equalitySymmetry functionEquality applyEquality because_Cache unionElimination promote_hyp hypothesis_subsumption productElimination voidEquality applyLambdaEquality imageMemberEquality baseClosed imageElimination addEquality dependent_set_memberEquality independent_pairFormation minusEquality intEquality instantiate cumulativity universeEquality

Latex:
\mforall{}[T,T':Type].  \mforall{}[l:T  List].  \mforall{}[b:T'].  \mforall{}[f:(T  List)  {}\mrightarrow{}  T'  {}\mrightarrow{}  T  {}\mrightarrow{}  T'].
(list-accum(t,a,h.f[t;a;h];b;l)  \mmember{}  T')

Date html generated: 2018_05_21-PM-00_19_07
Last ObjectModification: 2018_05_19-AM-06_59_01

Theory : list_0

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