### Nuprl Lemma : count-repeats_wf

`∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:T List].  (count-repeats(L,eq) ∈ (T × ℕ+) List)`

Proof

Definitions occuring in Statement :  count-repeats: `count-repeats(L,eq)` list: `T List` deq: `EqDecider(T)` nat_plus: `ℕ+` uall: `∀[x:A]. B[x]` member: `t ∈ T` product: `x:A × B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` count-repeats: `count-repeats(L,eq)` so_lambda: `λ2x y.t[x; y]` nat_plus: `ℕ+` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` true: `True` and: `P ∧ Q` prop: `ℙ` so_lambda: `λ2x.t[x]` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` not: `¬A` rev_implies: `P `` Q` implies: `P `` Q` false: `False` uiff: `uiff(P;Q)` uimplies: `b supposing a` subtract: `n - m` subtype_rel: `A ⊆r B` top: `Top` le: `A ≤ B` so_apply: `x[s]` so_apply: `x[s1;s2]`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality productEquality because_Cache hypothesis lambdaEquality dependent_set_memberEquality natural_numberEquality independent_pairFormation imageMemberEquality baseClosed addEquality setElimination rename dependent_functionElimination unionElimination lambdaFormation voidElimination productElimination independent_functionElimination independent_isectElimination applyEquality isect_memberEquality voidEquality intEquality minusEquality axiomEquality equalityTransitivity equalitySymmetry universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[L:T  List].    (count-repeats(L,eq)  \mmember{}  (T  \mtimes{}  \mBbbN{}\msupplus{})  List)

Date html generated: 2016_05_14-PM-03_22_55
Last ObjectModification: 2016_01_14-PM-11_23_17

Theory : decidable!equality

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