Nuprl Lemma : bag-append-assoc-comm
∀[T:Type]. ∀[as,bs,cs:bag(T)]. ((as + bs + cs) = (bs + as + cs) ∈ bag(T))
Proof
Definitions occuring in Statement :
bag-append: as + bs,
bag: bag(T),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
top: Top,
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
bag-append_wf,
squash_wf,
true_wf,
equal_wf,
bag_wf,
bag-append-comm,
iff_weakening_equal,
bag-append-assoc
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberEquality,
voidElimination,
voidEquality,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
cumulativity,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
isect_memberFormation,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs,cs:bag(T)]. ((as + bs + cs) = (bs + as + cs))
Date html generated:
2017_10_01-AM-08_45_03
Last ObjectModification:
2017_07_26-PM-04_30_29
Theory : bags
Home
Index