Nuprl Lemma : bag-append-comm
∀[T:Type]. ∀[as,bs:bag(T)]. ((as + bs) = (bs + as) ∈ 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,
bag: bag(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bag-append: as + bs,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
quotient-member-eq,
list_wf,
permutation_wf,
permutation-equiv,
append_wf,
permutation_functionality_wrt_permutation,
permutation_weakening,
append_functionality_wrt_permutation,
permutation_inversion,
permutation-rotate,
bag_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
because_Cache,
hypothesis,
sqequalRule,
pertypeElimination,
promote_hyp,
thin,
productElimination,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
lambdaFormation_alt,
rename,
extract_by_obid,
isectElimination,
hypothesisEquality,
lambdaEquality_alt,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
universeIsType,
equalityIstype,
productIsType,
sqequalBase,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:bag(T)]. ((as + bs) = (bs + as))
Date html generated:
2020_05_20-AM-08_01_29
Last ObjectModification:
2020_01_04-PM-11_16_43
Theory : bags
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