Nuprl Lemma : mset_union_mon_wf
∀s:DSet. (<MSet{s},⋃,0> ∈ AbMon)
Proof
Definitions occuring in Statement :
mset_union_mon: <MSet{s},⋃,0>,
all: ∀x:A. B[x],
member: t ∈ T,
abmonoid: AbMon,
dset: DSet
Definitions unfolded in proof :
mset_union_mon: <MSet{s},⋃,0>,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
assoc: Assoc(T;op),
infix_ap: x f y,
ident: Ident(T;op;id),
and: P ∧ Q,
comm: Comm(T;op)
Lemmas referenced :
mk_abmonoid,
mset_wf,
eq_mset_wf,
btrue_wf,
mset_union_wf,
null_mset_wf,
dset_wf,
mset_union_assoc,
mset_union_ident_r,
mset_union_ident_l,
mset_union_comm
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
lambdaEquality,
independent_isectElimination,
isect_memberFormation,
introduction,
isect_memberEquality,
axiomEquality,
because_Cache,
independent_pairFormation,
productElimination,
independent_pairEquality
Latex:
\mforall{}s:DSet. (<MSet\{s\},\mcup{},0> \mmember{} AbMon)
Date html generated:
2016_05_16-AM-07_49_30
Last ObjectModification:
2015_12_28-PM-06_01_27
Theory : mset
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