Nuprl Lemma : count_bsubmset
∀s:DSet. ∀a,b:MSet{s}. (↑(a ⊆b b) ⇐⇒ ∀x:|s|. ((x #∈ a) ≤ (x #∈ b)))
Proof
Definitions occuring in Statement :
bsubmset: a ⊆b b,
mset_count: x #∈ a,
mset: MSet{s},
assert: ↑b,
le: A ≤ B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
dset: DSet,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s],
implies: P ⇒ Q,
sq_stable: SqStable(P),
mset: MSet{s},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
prop: ℙ,
quotient: x,y:A//B[x; y],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
squash: ↓T,
mset_count: x #∈ a,
bsubmset: a ⊆b b
Lemmas referenced :
count_bsublist_a,
equal-wf-base,
permr_equiv_rel,
list_wf,
permr_wf,
subtype_quotient,
iff_wf,
squash_wf,
dset_wf,
mset_wf,
sq_stable__le,
sq_stable__all,
decidable__assert,
sq_stable_from_decidable,
nat_wf,
mset_count_wf,
le_wf,
set_car_wf,
all_wf,
bsubmset_wf,
assert_wf,
sq_stable__iff
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
lambdaEquality,
applyEquality,
because_Cache,
independent_functionElimination,
introduction,
pointwiseFunctionalityForEquality,
pertypeElimination,
productElimination,
independent_isectElimination,
imageMemberEquality,
baseClosed,
productEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}s:DSet. \mforall{}a,b:MSet\{s\}. (\muparrow{}(a \msubseteq{}\msubb{} b) \mLeftarrow{}{}\mRightarrow{} \mforall{}x:|s|. ((x \#\mmember{} a) \mleq{} (x \#\mmember{} b)))
Date html generated:
2016_05_16-AM-07_50_53
Last ObjectModification:
2016_01_16-PM-11_39_29
Theory : mset
Home
Index