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Step * of Lemma sub-bag-combine

∀[T,U:Type].  ∀f:T ⟶ bag(U). ∀b1,b2:bag(T).  (sub-bag(T;b1;b2) ⇒ sub-bag(U;⋃x∈b1.f[x];⋃x∈b2.f[x]))
BY
{ ((UnivCD THENA Auto)
   THEN Unfold `sub-bag` (-1)
   THEN ExRepD
   THEN (HypSubst' (-1) 0 THENA Auto)
   THEN (InstLemma `bag-combine-append-left` [⌜T⌝;⌜U⌝;⌜b1⌝;⌜cs⌝;⌜f⌝]⋅ THENA Auto)
   THEN (RWO "-1" 0 THENA Auto)
   THEN Unfold `sub-bag` 0
   THEN InstConcl [⌜⋃x∈cs.f[x]⌝]⋅
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[T,U:Type].    \mforall{}f:T  {}\mrightarrow{}  bag(U).  \mforall{}b1,b2:bag(T).    (sub-bag(T;b1;b2)  {}\mRightarrow{}  sub-bag(U;\mcup{}x\mmember{}b1.f[x];\mcup{}x\mmember{}b2.f[x]))


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  Unfold  `sub-bag`  (-1)
  THEN  ExRepD
  THEN  (HypSubst'  (-1)  0  THENA  Auto)
  THEN  (InstLemma  `bag-combine-append-left`  [\mkleeneopen{}T\mkleeneclose{};\mkleeneopen{}U\mkleeneclose{};\mkleeneopen{}b1\mkleeneclose{};\mkleeneopen{}cs\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  (RWO  "-1"  0  THENA  Auto)
  THEN  Unfold  `sub-bag`  0
  THEN  InstConcl  [\mkleeneopen{}\mcup{}x\mmember{}cs.f[x]\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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