Nuprl Lemma : no_repeats-bag
∀[T:Type]. ∀[as,bs:T List]. (no_repeats(T;as)) supposing (no_repeats(T;bs) and (as = bs ∈ bag(T)))
Proof
Definitions occuring in Statement :
bag: bag(T),
no_repeats: no_repeats(T;l),
list: T List,
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,
uimplies: b supposing a,
bag: bag(T),
quotient: x,y:A//B[x; y],
sq_stable: SqStable(P),
implies: P ⇒ Q,
all: ∀x:A. B[x],
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
list-subtype-bag,
bag_wf,
equal_wf,
no_repeats_wf,
no_repeats_witness,
permutation_wf,
list_wf,
member_wf,
and_wf,
no_repeats_functionality_wrt_permutation,
sq_stable__no_repeats
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
pertypeElimination,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
because_Cache,
dependent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
applyEquality,
independent_isectElimination,
lambdaEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:T List]. (no\_repeats(T;as)) supposing (no\_repeats(T;bs) and (as = bs))
Date html generated:
2016_05_15-PM-02_55_10
Last ObjectModification:
2016_01_16-AM-08_40_05
Theory : bags
Home
Index