Step * of Lemma setmem-transmem

x,y:coSet{i:l}.  ((x ∈ y)  (x ∈∈ y))
BY
(Auto
   THEN Unfold `transmem` 0
   THEN InstLemma `transitive-closure-contains` [⌜parm{i'}⌝;⌜coSet{i:l}⌝;⌜λx,y. (x ∈ y)⌝]⋅
   THEN Auto) }


Latex:


Latex:
\mforall{}x,y:coSet\{i:l\}.    ((x  \mmember{}  y)  {}\mRightarrow{}  (x  \mmember{}\mmember{}  y))


By


Latex:
(Auto
  THEN  Unfold  `transmem`  0
  THEN  InstLemma  `transitive-closure-contains`  [\mkleeneopen{}parm\{i'\}\mkleeneclose{};\mkleeneopen{}coSet\{i:l\}\mkleeneclose{};\mkleeneopen{}\mlambda{}x,y.  (x  \mmember{}  y)\mkleeneclose{}]\mcdot{}
  THEN  Auto)




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