Nuprl Lemma : bag-append-ac
∀[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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
squash: ↓T,
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_wf,
bag-append-assoc,
equal_wf,
squash_wf,
true_wf,
bag-append_wf,
bag-append-comm,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
universeEquality,
voidElimination,
voidEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination
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_06
Last ObjectModification:
2017_07_26-PM-04_30_33
Theory : bags
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