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Step * of Lemma bm_exists_downeq_wf

∀[T,Key:Type]. ∀[compare:bm_compare(Key)]. ∀[m:binary-map(T;Key)]. ∀[k:Key]. ∀[p:T ─→ 𝔹].
  (bm_exists_downeq(compare;m;k;p) ∈ 𝔹)
BY
{ (Auto
   THEN (InstLemma `binary_map_ind-wf2` [⌈𝔹⌉;⌈T⌉;⌈Key⌉]⋅ THENA Auto)
   THEN Unfold `bm_exists_downeq` 0
   THEN BHyp -1 
   THEN Auto) }

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Latex:


\mforall{}[T,Key:Type].  \mforall{}[compare:bm\_compare(Key)].  \mforall{}[m:binary-map(T;Key)].  \mforall{}[k:Key].  \mforall{}[p:T  {}\mrightarrow{}  \mBbbB{}].
    (bm\_exists\_downeq(compare;m;k;p)  \mmember{}  \mBbbB{})


By

(Auto
  THEN  (InstLemma  `binary\_map\_ind-wf2`  [\mkleeneopen{}\mBbbB{}\mkleeneclose{};\mkleeneopen{}T\mkleeneclose{};\mkleeneopen{}Key\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  Unfold  `bm\_exists\_downeq`  0
  THEN  BHyp  -1 
  THEN  Auto)

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