Nuprl Lemma : bag-remove-repeats-no-repeats
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)]. bag-no-repeats(T;bag-remove-repeats(eq;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),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
exists: ∃x:A. B[x],
bag-remove-repeats: bag-remove-repeats(eq;bs),
bag-no-repeats: bag-no-repeats(T;bs),
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
bag_to_squash_list,
sq_stable__bag-no-repeats,
bag-remove-repeats_wf,
list-to-set_wf,
list-subtype-bag,
list-to-set-property,
equal_wf,
bag_wf,
no_repeats_wf,
bag-no-repeats_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
imageElimination,
because_Cache,
cumulativity,
hypothesis,
independent_functionElimination,
productElimination,
promote_hyp,
rename,
dependent_pairFormation,
applyEquality,
independent_isectElimination,
lambdaEquality,
sqequalRule,
independent_pairFormation,
dependent_functionElimination,
productEquality,
imageMemberEquality,
baseClosed,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs:bag(T)]. bag-no-repeats(T;bag-remove-repeats(eq;bs))
Date html generated:
2018_05_21-PM-09_47_34
Last ObjectModification:
2017_07_26-PM-06_30_16
Theory : bags_2
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