Nuprl Lemma : bag-remove-repeats_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)]. (bag-remove-repeats(eq;bs) ∈ bag(T))
Proof
Definitions occuring in Statement :
bag-remove-repeats: bag-remove-repeats(eq;bs),
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
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,
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_wf,
quotient-member-eq,
permutation_wf,
permutation-equiv,
list-to-set_wf,
equal_wf,
equal-wf-base,
bag_wf,
deq_wf,
permutation_weakening,
permutation_functionality_wrt_permutation,
list-to-set_functionality_wrt_permutation
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
because_Cache,
sqequalRule,
pertypeElimination,
productElimination,
thin,
equalityTransitivity,
hypothesis,
equalitySymmetry,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
lambdaFormation,
rename,
lambdaEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
productEquality,
axiomEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs:bag(T)]. (bag-remove-repeats(eq;bs) \mmember{} bag(T))
Date html generated:
2018_05_21-PM-09_47_22
Last ObjectModification:
2017_07_26-PM-06_30_12
Theory : bags_2
Home
Index