Nuprl Lemma : mset_union_bor_mon_hom
∀s:DSet. ∀x:|s|. IsMonHom{<MSet{s},⋃,0>,<𝔹,∨b>}(λu.(x ∈b u))
Proof
Definitions occuring in Statement :
mset_union_mon: <MSet{s},⋃,0>,
mset_mem: mset_mem,
all: ∀x:A. B[x],
lambda: λx.A[x],
bor_mon: <𝔹,∨b>,
monoid_hom_p: IsMonHom{M1,M2}(f),
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
monoid_hom_p: IsMonHom{M1,M2}(f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
mset_union_mon: <MSet{s},⋃,0>,
grp_car: |g|,
pi1: fst(t),
bor_mon: <𝔹,∨b>,
grp_op: *,
pi2: snd(t),
grp_id: e,
infix_ap: x f y,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
dset: DSet
Lemmas referenced :
mset_mem_null_lemma,
mset_wf,
set_car_wf,
dset_wf,
fset_mem_union,
bfalse_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
lambdaFormation,
independent_pairFormation,
isect_memberFormation,
introduction,
hypothesisEquality,
isectElimination,
axiomEquality,
because_Cache,
setElimination,
rename
Latex:
\mforall{}s:DSet. \mforall{}x:|s|. IsMonHom\{<MSet\{s\},\mcup{},0>,<\mBbbB{},\mvee{}\msubb{}>\}(\mlambda{}u.(x \mmember{}\msubb{} u))
Date html generated:
2016_05_16-AM-07_49_51
Last ObjectModification:
2015_12_28-PM-06_01_06
Theory : mset
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