Nuprl Lemma : bag-remove-repeats-eq-remove-repeats
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)]. (bag-remove-repeats(eq;bs) = remove-repeats(eq;bs) ∈ bag(T))
Proof
Definitions occuring in Statement :
bag-remove-repeats: bag-remove-repeats(eq;bs),
bag: bag(T),
remove-repeats: remove-repeats(eq;L),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag: bag(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bag-remove-repeats: bag-remove-repeats(eq;bs),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
quotient-member-eq,
list_wf,
permutation_wf,
permutation-equiv,
list-to-set_wf,
remove-repeats_wf,
permutation_functionality_wrt_permutation,
permutation_weakening,
remove-repeats_functionality_wrt_permutation,
permutation_inversion,
list-to-set-is-remove-repeats,
bag_wf,
deq_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
because_Cache,
hypothesis,
sqequalRule,
pertypeElimination,
promote_hyp,
thin,
productElimination,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
lambdaFormation_alt,
rename,
extract_by_obid,
isectElimination,
hypothesisEquality,
lambdaEquality_alt,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
universeIsType,
equalityIstype,
productIsType,
sqequalBase,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs:bag(T)]. (bag-remove-repeats(eq;bs) = remove-repeats(eq;bs))
Date html generated:
2020_05_20-AM-09_04_15
Last ObjectModification:
2020_01_04-PM-10_17_54
Theory : bags_2
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