### 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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