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
Lemmas referenced :
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,
no_repeats-update-alist,
deq_wf,
no_repeats_witness,
list_accum_cons_lemma,
top_wf,
subtype_rel_list,
list_accum_append,
no_repeats_nil,
map_nil_lemma,
list_accum_nil_lemma,
list_wf,
count-repeats_wf,
pi1_wf,
nat_plus_wf,
map_wf,
no_repeats_wf,
last_induction
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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