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Step * of Lemma bag-remove-repeats-if-no-repeats

∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)].  bag-remove-repeats(eq;bs) = bs ∈ bag(T) supposing bag-no-repeats(T;bs)
BY
{ ((UnivCD THENA Auto)
   THEN (BagToList (-2) THENA Auto)
   THEN (RWO "bag-no-repeats-list" (-1) THENA Auto)
   THEN RepUR ``bag-remove-repeats`` 0
   THEN RWO "no-repeats-list-to-set" 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[bs:bag(T)].
    bag-remove-repeats(eq;bs)  =  bs  supposing  bag-no-repeats(T;bs)


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  (BagToList  (-2)  THENA  Auto)
  THEN  (RWO  "bag-no-repeats-list"  (-1)  THENA  Auto)
  THEN  RepUR  ``bag-remove-repeats``  0
  THEN  RWO  "no-repeats-list-to-set"  0
  THEN  Auto)

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