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Step * of Lemma dl-valid-box-choose-dist-and

∀a,b:Prog. ∀phi:Prop.  (|= [a ⋃ b] phi ⇒ |= [a] phi ∧ [b] phi)
BY
{ (((Auto THEN ParallelLast) THEN Auto)
   THEN (InstHyp [⌜K⌝;⌜R⌝;⌜P⌝;⌜k⌝] (4)⋅ THEN Auto)
   THEN All DlSemReduce
   THEN Auto) }

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Latex:

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Latex:
\mforall{}a,b:Prog.  \mforall{}phi:Prop.    (|=  [a  \mcup{}  b]  phi  {}\mRightarrow{}  |=  [a]  phi  \mwedge{}  [b]  phi)


By

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Latex:
(((Auto  THEN  ParallelLast)  THEN  Auto)
  THEN  (InstHyp  [\mkleeneopen{}K\mkleeneclose{};\mkleeneopen{}R\mkleeneclose{};\mkleeneopen{}P\mkleeneclose{};\mkleeneopen{}k\mkleeneclose{}]  (4)\mcdot{}  THEN  Auto)
  THEN  All  DlSemReduce
  THEN  Auto)

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