Nuprl Lemma : remove-repeats-wf-bag
∀[T:Type]. ∀eq:EqDecider(T). ∀bs:bag(T). (remove-repeats(eq;bs) ∈ bag(T))
Proof
Definitions occuring in Statement :
bag: bag(T),
remove-repeats: remove-repeats(eq;L),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
bag: bag(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
quotient-member-eq,
permutation_wf,
list_wf,
permutation-equiv,
remove-repeats_wf,
remove-repeats_functionality_wrt_permutation,
equal-wf-base,
bag_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
because_Cache,
sqequalRule,
pertypeElimination,
productElimination,
thin,
lemma_by_obid,
isectElimination,
lambdaEquality,
hypothesisEquality,
hypothesis,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
productEquality,
cumulativity,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}eq:EqDecider(T). \mforall{}bs:bag(T). (remove-repeats(eq;bs) \mmember{} bag(T))
Date html generated:
2016_05_15-PM-02_56_25
Last ObjectModification:
2015_12_27-AM-09_31_23
Theory : bags
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