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Step * 1 1 of Lemma sdata_atoms_pair_lemma


1. d2 : Top@i
2. d1 : Top@i
⊢ tree_ind(d1;
           tree_leaf(value)⇒ if ¬bisl(value) then [outr(value)] else [] fi ;
           tree_node(left,right)⇒ rec1,rec2.rec1 @ rec2) 
@ tree_ind(d2;
           tree_leaf(value)⇒ if ¬bisl(value) then [outr(value)] else [] fi ;
           tree_node(left,right)⇒ rec1,rec2.rec1 @ rec2)  ~ sdata-atoms(d1) @ sdata-atoms(d2)
BY
{ Try (RW (AddrC [2] (UnfoldC `sdata-atoms`)) 0)⋅ }

1
1. d2 : Top@i
2. d1 : Top@i
⊢ tree_ind(d1;
           tree_leaf(value)⇒ if ¬bisl(value) then [outr(value)] else [] fi ;
           tree_node(left,right)⇒ rec1,rec2.rec1 @ rec2) 
@ tree_ind(d2;
           tree_leaf(value)⇒ if ¬bisl(value) then [outr(value)] else [] fi ;
           tree_node(left,right)⇒ rec1,rec2.rec1 @ rec2)  ~ tree_ind(d1;
                                                                      tree_leaf(x)⇒ if ¬bisl(x)
                                                                      then [outr(x)]
                                                                      else []
                                                                      fi ;
                                                                      tree_node(x,y)⇒ as,bs.as @ bs) 
@ tree_ind(d2;
           tree_leaf(x)⇒ if ¬bisl(x) then [outr(x)] else [] fi ;
           tree_node(x,y)⇒ as,bs.as @ bs) 

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Latex:

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Latex:

1.  d2  :  Top@i
2.  d1  :  Top@i
\mvdash{}  tree\_ind(d1;
                      tree\_leaf(value){}\mRightarrow{}  if  \mneg{}\msubb{}isl(value)  then  [outr(value)]  else  []  fi  ;
                      tree\_node(left,right){}\mRightarrow{}  rec1,rec2.rec1  @  rec2) 
@  tree\_ind(d2;
                      tree\_leaf(value){}\mRightarrow{}  if  \mneg{}\msubb{}isl(value)  then  [outr(value)]  else  []  fi  ;
                      tree\_node(left,right){}\mRightarrow{}  rec1,rec2.rec1  @  rec2)    \msim{}  sdata-atoms(d1)  @  sdata-atoms(d2)


By

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Latex:
Try  (RW  (AddrC  [2]  (UnfoldC  `sdata-atoms`))  0)\mcdot{}

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