### Nuprl Lemma : lifting-bag-combine-decide-name_eq

`∀[a,b,F,G,f:Top].`
`  (⋃b∈case name_eq(a;b) of inl(x) => F[x] | inr(x) => G[x].f[b] ~ case name_eq(a;b)`
`   of inl(x) =>`
`   ⋃b∈F[x].f[b]`
`   | inr(x) =>`
`   ⋃b∈G[x].f[b])`

Proof

Definitions occuring in Statement :  bag-combine: `⋃x∈bs.f[x]` name_eq: `name_eq(x;y)` uall: `∀[x:A]. B[x]` top: `Top` so_apply: `x[s]` decide: `case b of inl(x) => s[x] | inr(y) => t[y]` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` top: `Top` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  lifting-bag-combine-decide top_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity cut lemma_by_obid sqequalHypSubstitution sqequalTransitivity computationStep isectElimination thin isect_memberEquality voidElimination voidEquality hypothesis isect_memberFormation introduction sqequalAxiom hypothesisEquality because_Cache

Latex:
\mforall{}[a,b,F,G,f:Top].
(\mcup{}b\mmember{}case  name\_eq(a;b)  of  inl(x)  =>  F[x]  |  inr(x)  =>  G[x].f[b]  \msim{}  case  name\_eq(a;b)
of  inl(x)  =>
\mcup{}b\mmember{}F[x].f[b]
|  inr(x)  =>
\mcup{}b\mmember{}G[x].f[b])

Date html generated: 2016_05_15-PM-03_10_20
Last ObjectModification: 2015_12_27-AM-09_25_11

Theory : bags

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