### Nuprl Lemma : list-subtype

`∀[A:Type]. ∀[d:A List].  (d ∈ {a:A| (a ∈ d)}  List)`

Proof

Definitions occuring in Statement :  l_member: `(x ∈ l)` list: `T List` uall: `∀[x:A]. B[x]` member: `t ∈ T` set: `{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` 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` 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 cut thin lambdaFormation introduction extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination natural_numberEquality independent_isectElimination independent_functionElimination voidElimination lambdaEquality dependent_functionElimination axiomEquality equalityTransitivity equalitySymmetry applyEquality because_Cache unionElimination setEquality promote_hyp hypothesis_subsumption productElimination isect_memberEquality voidEquality applyLambdaEquality imageMemberEquality baseClosed imageElimination addEquality dependent_set_memberEquality independent_pairFormation minusEquality intEquality instantiate cumulativity inlFormation universeEquality inrFormation

Latex:
\mforall{}[A:Type].  \mforall{}[d:A  List].    (d  \mmember{}  \{a:A|  (a  \mmember{}  d)\}    List)

Date html generated: 2018_05_21-PM-00_19_18
Last ObjectModification: 2018_05_19-AM-06_59_20

Theory : list_0

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