Nuprl Lemma : bag-union-as-combine
∀[A:Type]. ∀[x:bag(bag(A))]. (bag-union(x) = ⋃b∈x.b ∈ bag(A))
Proof
Definitions occuring in Statement :
bag-combine: ⋃x∈bs.f[x],
bag-union: bag-union(bbs),
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-combine: ⋃x∈bs.f[x],
squash: ↓T,
prop: ℙ,
uimplies: b supposing a,
all: ∀x:A. B[x],
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
bag_wf,
bag-union_wf,
bag-map-trivial,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
because_Cache,
independent_isectElimination,
lambdaFormation,
natural_numberEquality,
imageMemberEquality,
baseClosed,
instantiate,
productElimination,
independent_functionElimination,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[A:Type]. \mforall{}[x:bag(bag(A))]. (bag-union(x) = \mcup{}b\mmember{}x.b)
Date html generated:
2018_05_21-PM-06_24_14
Last ObjectModification:
2018_05_19-PM-05_15_11
Theory : bags
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