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]
Lemmas referenced :
deq_wf,
le-add-cancel,
add-zero,
add-associates,
add_functionality_wrt_le,
add-commutes,
minus-one-mul-top,
zero-add,
minus-one-mul,
minus-add,
condition-implies-le,
less-iff-le,
not-lt-2,
false_wf,
decidable__lt,
less_than_wf,
update-alist_wf,
nil_wf,
nat_plus_wf,
list_wf,
list_accum_wf
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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