Nuprl Lemma : mset_size_wf
∀s:DSet. ∀a:MSet{s}.  (size{s}(a) ∈ ℤ)
Proof
Definitions occuring in Statement : 
mset_size: size{s}(a)
, 
mset: MSet{s}
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
int: ℤ
, 
dset: DSet
Definitions unfolded in proof : 
mset_size: size{s}(a)
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
mset: MSet{s}
, 
quotient: x,y:A//B[x; y]
, 
and: P ∧ Q
, 
uall: ∀[x:A]. B[x]
, 
dset: DSet
, 
implies: P 
⇒ Q
, 
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 : 
mset_wf, 
dset_wf, 
list_wf, 
set_car_wf, 
permr_wf, 
equal_wf, 
equal-wf-base, 
squash_wf, 
true_wf, 
length_functionality_wrt_permr, 
length_wf, 
iff_weakening_equal
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
lambdaFormation, 
cut, 
sqequalHypSubstitution, 
hypothesis, 
introduction, 
extract_by_obid, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
pointwiseFunctionalityForEquality, 
intEquality, 
pertypeElimination, 
productElimination, 
equalityTransitivity, 
equalitySymmetry, 
isectElimination, 
setElimination, 
rename, 
because_Cache, 
independent_functionElimination, 
productEquality, 
applyEquality, 
lambdaEquality, 
imageElimination, 
universeEquality, 
natural_numberEquality, 
imageMemberEquality, 
baseClosed, 
independent_isectElimination
Latex:
\mforall{}s:DSet.  \mforall{}a:MSet\{s\}.    (size\{s\}(a)  \mmember{}  \mBbbZ{})
Date html generated:
2017_10_01-AM-09_59_29
Last ObjectModification:
2017_03_03-PM-01_00_29
Theory : mset
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