### Nuprl Lemma : no_repeats-count-repeats1

`∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:T List].  no_repeats(T;map(λp.(fst(p));count-repeats(L,eq)))`

Proof

Definitions occuring in Statement :  count-repeats: `count-repeats(L,eq)` no_repeats: `no_repeats(T;l)` map: `map(f;as)` list: `T List` deq: `EqDecider(T)` uall: `∀[x:A]. B[x]` pi1: `fst(t)` lambda: `λx.A[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` so_apply: `x[s]` implies: `P `` Q` count-repeats: `count-repeats(L,eq)` all: `∀x:A. B[x]` top: `Top` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` subtype_rel: `A ⊆r B` uimplies: `b supposing a` prop: `ℙ` guard: `{T}` nat_plus: `ℕ+` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` true: `True` and: `P ∧ Q` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` not: `¬A` rev_implies: `P `` Q` false: `False` uiff: `uiff(P;Q)` subtract: `n - m` le: `A ≤ B`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin lemma_by_obid sqequalHypSubstitution isectElimination hypothesisEquality sqequalRule lambdaEquality productEquality hypothesis independent_functionElimination dependent_functionElimination isect_memberEquality voidElimination voidEquality lambdaFormation applyEquality because_Cache independent_isectElimination universeEquality dependent_set_memberEquality natural_numberEquality independent_pairFormation imageMemberEquality baseClosed addEquality setElimination rename unionElimination productElimination intEquality minusEquality

Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[L:T  List].    no\_repeats(T;map(\mlambda{}p.(fst(p));count-repeats(L,eq)))

Date html generated: 2016_05_14-PM-03_22_56
Last ObjectModification: 2016_01_14-PM-11_23_23

Theory : decidable!equality

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