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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