Nuprl Lemma : bsubmset_elim
∀s:DSet. ∀as,bs:|s| List. mk_mset(as) ⊆b mk_mset(bs) = bsublist(s;as;bs)
Proof
Definitions occuring in Statement :
bsubmset: a ⊆b b,
mk_mset: mk_mset(as),
bsublist: bsublist(s;as;bs),
list: T List,
bool: 𝔹,
all: ∀x:A. B[x],
equal: s = t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
mk_mset: mk_mset(as),
bsubmset: a ⊆b b,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet
Lemmas referenced :
bsublist_wf,
list_wf,
set_car_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
isectElimination,
setElimination,
rename
Latex:
\mforall{}s:DSet. \mforall{}as,bs:|s| List. mk\_mset(as) \msubseteq{}\msubb{} mk\_mset(bs) = bsublist(s;as;bs)
Date html generated:
2016_05_16-AM-07_50_42
Last ObjectModification:
2015_12_28-PM-06_00_33
Theory : mset
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