Nuprl Lemma : bag-union-append
∀[A:Type]. ∀[b1,b2:bag(bag(A))]. (bag-union(b1 + b2) = (bag-union(b1) + bag-union(b2)) ∈ bag(A))
Proof
Definitions occuring in Statement :
bag-union: bag-union(bbs),
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,
squash: ↓T,
prop: ℙ,
all: ∀x:A. B[x],
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 :
equal_wf,
squash_wf,
true_wf,
bag_wf,
bag-append-union,
bag-append_wf,
bag-union_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
dependent_functionElimination,
cumulativity,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[A:Type]. \mforall{}[b1,b2:bag(bag(A))]. (bag-union(b1 + b2) = (bag-union(b1) + bag-union(b2)))
Date html generated:
2017_10_01-AM-08_47_01
Last ObjectModification:
2017_07_26-PM-04_31_42
Theory : bags
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