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Step * of Lemma trans-id-property

∀C1,C2:SmallCategory. ∀x,y:Functor(C1;C2). ∀f:nat-trans(C1;C2;x;y).
  ((trans-comp(C1;C2;x;x;y;identity-trans(C1;C2;x);f) = f ∈ nat-trans(C1;C2;x;y))
  ∧ (trans-comp(C1;C2;x;y;y;f;identity-trans(C1;C2;y)) = f ∈ nat-trans(C1;C2;x;y)))
BY
{ (Auto
   THEN DVar `f'
   THEN Symmetry
   THEN EqTypeCD
   THEN Auto
   THEN Ext
   THEN Auto
   THEN RepUR ``trans-comp identity-trans`` 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}C1,C2:SmallCategory.  \mforall{}x,y:Functor(C1;C2).  \mforall{}f:nat-trans(C1;C2;x;y).
    ((trans-comp(C1;C2;x;x;y;identity-trans(C1;C2;x);f)  =  f)
    \mwedge{}  (trans-comp(C1;C2;x;y;y;f;identity-trans(C1;C2;y))  =  f))


By

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Latex:
(Auto
  THEN  DVar  `f'
  THEN  Symmetry
  THEN  EqTypeCD
  THEN  Auto
  THEN  Ext
  THEN  Auto
  THEN  RepUR  ``trans-comp  identity-trans``  0
  THEN  Auto)

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