Nuprl Lemma : fset_mem_union
∀s:DSet. ∀as,bs:MSet{s}. ∀c:|s|. c ∈b as ⋃ bs = (c ∈b as) ∨b(c ∈b bs)
Proof
Definitions occuring in Statement :
mset_union: a ⋃ b,
mset_mem: mset_mem,
mset: MSet{s},
bor: p ∨bq,
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_union: a ⋃ 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
Lemmas referenced :
mem_lmax,
set_car_wf,
list_wf,
all_mset_elim,
all_wf,
equal_wf,
bool_wf,
mset_mem_wf,
mset_union_wf,
mk_mset_wf,
bor_wf,
mset_wf,
sq_stable__all,
sq_stable__equal,
mem_wf,
lmax_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
isectElimination,
setElimination,
rename,
addLevel,
sqequalRule,
allFunctionality,
lambdaEquality,
because_Cache,
independent_functionElimination,
productElimination,
levelHypothesis,
allLevelFunctionality
Latex:
\mforall{}s:DSet. \mforall{}as,bs:MSet\{s\}. \mforall{}c:|s|. c \mmember{}\msubb{} as \mcup{} bs = (c \mmember{}\msubb{} as) \mvee{}\msubb{}(c \mmember{}\msubb{} bs)
Date html generated:
2018_05_22-AM-07_45_52
Last ObjectModification:
2018_05_19-AM-08_30_59
Theory : mset
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