Nuprl Lemma : mset_count_diff
∀s:DSet. ∀as,bs:MSet{s}. ∀c:|s|. ((c #∈ (as - bs)) = ((c #∈ as) -- (c #∈ bs)) ∈ ℤ)
Proof
Definitions occuring in Statement :
mset_diff: a - b,
mset_count: x #∈ a,
mset: MSet{s},
ndiff: 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_diff: a - b,
prop: ℙ,
true: True,
squash: ↓T,
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,
diff_wf,
ndiff_wf,
count_wf,
count_diff,
iff_weakening_equal,
squash_wf,
true_wf,
count_functionality,
diff_functionality_wrt_permr
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,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
imageMemberEquality,
baseClosed,
independent_isectElimination,
universeEquality
Latex:
\mforall{}s:DSet. \mforall{}as,bs:MSet\{s\}. \mforall{}c:|s|. ((c \#\mmember{} (as - bs)) = ((c \#\mmember{} as) -- (c \#\mmember{} bs)))
Date html generated:
2017_10_01-AM-10_00_04
Last ObjectModification:
2017_03_03-PM-01_01_25
Theory : mset
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