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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