Step 
*
 of Lemma 
compose-rotate-by
∀[n,i,j:ℕ].  ((rotate-by(n;i) o rotate-by(n;j)) = rotate-by(n;i + j) ∈ (ℕn ⟶ ℕn))
BY
 
{ xxx(Auto THEN RWO "iterate-rotate-rotate-by<" 0 THEN Auto' THEN RWO "fun_exp_add" 0 THEN Auto)xxx }
 
Latex: 
Latex:
\mforall{}[n,i,j:\mBbbN{}].    ((rotate-by(n;i)  o  rotate-by(n;j))  =  rotate-by(n;i  +  j))
 By 
Latex:
xxx(Auto  THEN  RWO  "iterate-rotate-rotate-by<"  0  THEN  Auto'  THEN  RWO  "fun\_exp\_add"  0  THEN  Auto)xxx
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