Nuprl Lemma : bag-remove-repeats-if-no-repeats
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)]. bag-remove-repeats(eq;bs) = bs ∈ bag(T) supposing bag-no-repeats(T;bs)
Proof
Definitions occuring in Statement :
bag-remove-repeats: bag-remove-repeats(eq;bs),
bag-no-repeats: bag-no-repeats(T;bs),
bag: bag(T),
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
exists: ∃x:A. B[x],
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bag-remove-repeats: bag-remove-repeats(eq;bs),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
bag_to_squash_list,
bag-no-repeats_wf,
bag-no-repeats-list,
no-repeats-list-to-set,
list-subtype-bag,
equal_wf,
bag_wf,
bag-remove-repeats_wf,
deq_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
imageElimination,
productElimination,
promote_hyp,
hypothesis,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality,
cumulativity,
sqequalRule,
rename,
independent_isectElimination,
dependent_functionElimination,
applyEquality,
because_Cache,
lambdaEquality,
universeEquality,
isect_memberFormation,
isect_memberEquality,
axiomEquality,
equalityTransitivity
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs:bag(T)].
bag-remove-repeats(eq;bs) = bs supposing bag-no-repeats(T;bs)
Date html generated:
2016_10_25-AM-11_26_52
Last ObjectModification:
2016_07_12-AM-07_33_16
Theory : bags_2
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