Nuprl Lemma : count_bsublist
∀s:DSet. ∀as,bs:|s| List. (↑bsublist(s;as;bs) ⇐⇒ {∀c:|s|. ((c #∈ as) ≤ (c #∈ bs))})
Proof
Definitions occuring in Statement :
bsublist: bsublist(s;as;bs),
count: a #∈ as,
list: T List,
assert: ↑b,
guard: {T},
le: A ≤ B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
guard: {T},
bsublist: bsublist(s;as;bs),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
prop: ℙ,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
top: Top,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
set_car_wf,
assert_wf,
null_wf,
diff_wf,
le_wf,
count_wf,
list_wf,
dset_wf,
assert_of_null,
equal_wf,
squash_wf,
true_wf,
istype-universe,
count_diff,
subtype_rel_self,
iff_weakening_equal,
count_nil_lemma,
istype-void,
ndiff_zero,
nil_wf,
permr_nil_is_nil,
permr_iff_eq_counts
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation_alt,
independent_pairFormation,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
functionIsType,
because_Cache,
inhabitedIsType,
productElimination,
independent_isectElimination,
applyLambdaEquality,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
intEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
instantiate,
independent_functionElimination,
isect_memberEquality_alt,
voidElimination
Latex:
\mforall{}s:DSet. \mforall{}as,bs:|s| List. (\muparrow{}bsublist(s;as;bs) \mLeftarrow{}{}\mRightarrow{} \{\mforall{}c:|s|. ((c \#\mmember{} as) \mleq{} (c \#\mmember{} bs))\})
Date html generated:
2019_10_16-PM-01_05_05
Last ObjectModification:
2018_10_08-AM-11_18_32
Theory : list_2
Home
Index