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Step * of Lemma bag-eq-subtype

∀[A:Type]. ∀[d1,d2:bag(A)].  d1 = d2 ∈ bag({a:A| a ↓∈ d1} ) supposing d1 = d2 ∈ bag(A)
BY
{ ((UnivCD THENA Auto)
   THEN InstLemma `bag-eq-subtype1` [⌜A⌝;⌜λa.a ↓∈ d1⌝;⌜d1⌝;⌜d2⌝]⋅
   THEN All (RepUR ``so_apply``)
   THEN Auto
   THEN Try (Complete ((BLemma `bag-subtype` THEN Auto)))
   THEN (InstLemma `bag-subtype` [⌜A⌝;⌜d2⌝]⋅ THENA Auto)
   THEN (Assert ⌜{x:A| x ↓∈ d2}  = {a:A| a ↓∈ d1}  ∈ Type⌝⋅ THENA (HypSubst' (-2) 0 THEN Auto))
   THEN RWO "-1" (-2)
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[A:Type].  \mforall{}[d1,d2:bag(A)].    d1  =  d2  supposing  d1  =  d2


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  InstLemma  `bag-eq-subtype1`  [\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}\mlambda{}a.a  \mdownarrow{}\mmember{}  d1\mkleeneclose{};\mkleeneopen{}d1\mkleeneclose{};\mkleeneopen{}d2\mkleeneclose{}]\mcdot{}
  THEN  All  (RepUR  ``so\_apply``)
  THEN  Auto
  THEN  Try  (Complete  ((BLemma  `bag-subtype`  THEN  Auto)))
  THEN  (InstLemma  `bag-subtype`  [\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}d2\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  (Assert  \mkleeneopen{}\{x:A|  x  \mdownarrow{}\mmember{}  d2\}    =  \{a:A|  a  \mdownarrow{}\mmember{}  d1\}  \mkleeneclose{}\mcdot{}  THENA  (HypSubst'  (-2)  0  THEN  Auto))
  THEN  RWO  "-1"  (-2)
  THEN  Auto)

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