Nuprl Lemma : bag-monoid_wf
∀[T:Type]. (bag-monoid(T) ∈ AbMon)
Proof
Definitions occuring in Statement : 
bag-monoid: bag-monoid(T)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
universe: Type
, 
abmonoid: AbMon
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
bag-monoid: bag-monoid(T)
, 
assoc: Assoc(T;op)
, 
infix_ap: x f y
, 
top: Top
, 
ident: Ident(T;op;id)
, 
all: ∀x:A. B[x]
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
comm: Comm(T;op)
, 
uimplies: b supposing a
Lemmas referenced : 
bag_wf, 
btrue_wf, 
bag-append_wf, 
empty-bag_wf, 
bag-append-assoc2, 
empty_bag_append_lemma, 
bag-append-ident, 
bag-append-comm, 
mk_abmonoid
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalHypSubstitution, 
hypothesis, 
sqequalRule, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality, 
extract_by_obid, 
isectElimination, 
thin, 
hypothesisEquality, 
lambdaEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
because_Cache, 
dependent_functionElimination, 
productElimination, 
independent_pairFormation, 
independent_pairEquality, 
independent_isectElimination
Latex:
\mforall{}[T:Type].  (bag-monoid(T)  \mmember{}  AbMon)
Date html generated:
2019_10_15-AM-11_05_34
Last ObjectModification:
2018_09_24-PM-03_36_58
Theory : bags
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