Nuprl Lemma : bag-separate_wf
∀[A,B:Type]. ∀[bs:bag(A + B)]. (bag-separate(bs) ∈ bag(A) × bag(B))
Proof
Definitions occuring in Statement :
bag-separate: bag-separate(bs),
bag: bag(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-separate: bag-separate(bs),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
prop: ℙ,
outl: outl(x),
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
outr: outr(x),
bnot: ¬bb,
btrue: tt
Lemmas referenced :
bag-mapfilter_wf,
isl_wf,
assert_wf,
top_wf,
subtype_rel_union,
bnot_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
independent_pairEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
cumulativity,
hypothesisEquality,
because_Cache,
dependent_functionElimination,
lambdaEquality,
hypothesis,
lambdaFormation,
applyEquality,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
setElimination,
rename,
unionElimination,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[bs:bag(A + B)]. (bag-separate(bs) \mmember{} bag(A) \mtimes{} bag(B))
Date html generated:
2016_05_15-PM-02_35_30
Last ObjectModification:
2015_12_27-AM-09_45_43
Theory : bags
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