Nuprl Lemma : mset_mem_iff_count_nzero
∀s:DSet. ∀x:|s|. ∀a:MSet{s}. (↑(x ∈b a) ⇐⇒ (x #∈ a) > 0)
Proof
Definitions occuring in Statement :
mset_mem: mset_mem,
mset_count: x #∈ a,
mset: MSet{s},
assert: ↑b,
gt: i > j,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
natural_number: $n,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
nat: ℕ,
implies: P ⇒ Q,
gt: i > j,
sq_stable: SqStable(P),
dset: DSet,
mset: MSet{s},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
prop: ℙ,
quotient: x,y:A//B[x; y],
mset_count: x #∈ a,
mset_mem: mset_mem,
squash: ↓T
Lemmas referenced :
sq_stable__iff,
assert_wf,
mset_mem_wf,
gt_wf,
mset_count_wf,
nat_wf,
sq_stable_from_decidable,
decidable__assert,
sq_stable__less_than,
mset_wf,
set_car_wf,
dset_wf,
squash_wf,
iff_wf,
list_wf,
permr_wf,
equal_wf,
equal-wf-base,
mem_iff_count_nzero
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
natural_numberEquality,
independent_functionElimination,
because_Cache,
pointwiseFunctionalityForEquality,
pertypeElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
productEquality
Latex:
\mforall{}s:DSet. \mforall{}x:|s|. \mforall{}a:MSet\{s\}. (\muparrow{}(x \mmember{}\msubb{} a) \mLeftarrow{}{}\mRightarrow{} (x \#\mmember{} a) > 0)
Date html generated:
2017_10_01-AM-09_59_09
Last ObjectModification:
2017_03_03-PM-01_00_03
Theory : mset
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