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

`∀[a,F,G,f:Top].`
`  (⋃b∈case a of inl(x) => F[x] | inr(x) => G[x].f[b] ~ case a 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]` 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 :  member: `t ∈ T` top: `Top` uall: `∀[x:A]. B[x]` so_lambda: `so_lambda(x,y,z,w.t[x; y; z; w])` so_apply: `x[s1;s2;s3;s4]` uimplies: `b supposing a`
Lemmas referenced :  lifting-strict-decide top_wf strict4-bag-combine
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity thin baseClosed hypothesisEquality isect_memberEquality voidElimination voidEquality cut lemma_by_obid hypothesis because_Cache isect_memberFormation introduction sqequalAxiom sqequalRule sqequalHypSubstitution isectElimination independent_isectElimination

Latex:
\mforall{}[a,F,G,f:Top].
(\mcup{}b\mmember{}case  a  of  inl(x)  =>  F[x]  |  inr(x)  =>  G[x].f[b]  \msim{}  case  a
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_09_47
Last ObjectModification: 2016_01_16-AM-08_33_50

Theory : bags

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