Nuprl Lemma : mset_count_inter
∀s:DSet. ∀as,bs:MSet{s}. ∀c:|s|. ((c #∈ (as ⋂s bs)) = imin(c #∈ as;c #∈ bs) ∈ ℤ)
Proof
Definitions occuring in Statement :
mset_inter: a ⋂s b,
mset_count: x #∈ a,
mset: MSet{s},
imin: imin(a;b),
all: ∀x:A. B[x],
int: ℤ,
equal: s = t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
mset: MSet{s},
quotient: x,y:A//B[x; y],
and: P ∧ Q,
implies: P ⇒ Q,
mset_count: x #∈ a,
mset_inter: a ⋂s b,
prop: ℙ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
set_car_wf,
mset_wf,
dset_wf,
list_wf,
permr_wf,
equal_wf,
equal-wf-base,
squash_wf,
true_wf,
count_functionality,
lmin_wf,
lmin_functionality_wrt_permr,
imin_wf,
count_wf,
iff_weakening_equal,
count_lmin
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
dependent_functionElimination,
pointwiseFunctionalityForEquality,
intEquality,
sqequalRule,
pertypeElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
independent_functionElimination,
productEquality,
applyEquality,
lambdaEquality,
imageElimination,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination
Latex:
\mforall{}s:DSet. \mforall{}as,bs:MSet\{s\}. \mforall{}c:|s|. ((c \#\mmember{} (as \mcap{}s bs)) = imin(c \#\mmember{} as;c \#\mmember{} bs))
Date html generated:
2017_10_01-AM-10_00_01
Last ObjectModification:
2017_03_03-PM-01_00_54
Theory : mset
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