Nuprl Lemma : mset_mem_inter
∀s:DSet. ∀as,bs:MSet{s}. ∀c:|s|. c ∈b as ⋂s bs = (c ∈b as) ∧b (c ∈b bs)
Proof
Definitions occuring in Statement :
mset_inter: a ⋂s b,
mset_mem: mset_mem,
mset: MSet{s},
band: p ∧b q,
bool: 𝔹,
all: ∀x:A. B[x],
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,
mk_mset: mk_mset(as),
mset_inter: a ⋂s b,
mset_mem: mset_mem,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
bfalse: ff
Lemmas referenced :
set_car_wf,
list_wf,
all_mset_elim,
all_wf,
equal_wf,
bool_wf,
mset_mem_wf,
mset_inter_wf,
mk_mset_wf,
band_wf,
mset_wf,
sq_stable__all,
sq_stable__equal,
mem_wf,
lmin_wf,
eqtt_to_assert,
dset_wf,
mem_lmin
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
addLevel,
sqequalRule,
allFunctionality,
dependent_functionElimination,
lambdaEquality,
because_Cache,
independent_functionElimination,
productElimination,
levelHypothesis,
allLevelFunctionality,
unionElimination,
equalityElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}s:DSet. \mforall{}as,bs:MSet\{s\}. \mforall{}c:|s|. c \mmember{}\msubb{} as \mcap{}s bs = (c \mmember{}\msubb{} as) \mwedge{}\msubb{} (c \mmember{}\msubb{} bs)
Date html generated:
2017_10_01-AM-10_00_06
Last ObjectModification:
2017_03_03-PM-01_01_39
Theory : mset
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