Make sense of the apparent gibberish in “A Logical Approach to Discrete Math” Ch.0

apparent-gibberish.md

Every value in array segment b[1..n] that is not in b[i..j] is in b[i..j].

Let predicate p(v) be "v is in b[i..j]."

  (A k: 0<k<=N: ~p(b[k]) -> p(b[k]))
=
  (A k: 0<k<=N: ~~p(b[k]) | p(b[k]))
=
  (A k: 0<k<=N: p(b[k]) | p(b[k]))
=
  (A k: 0<k<=N: p(b[k]))

Every value in array segment b[1..n] that is in b[i..j].