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Proof step 2 from proof pos-at (previous step)

n < # str ⊦ pos(s→l(str)[n], str) = n, str = "", dups(s→l(str))

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ n. n < # str0 → pos(s→l(str0)[n], str0) = n ∨ str0 = "" ∨ dups(s→l(str0)), n < #(char + str0) ⊦ pos(s→l(char + str0)[n], char + str0) = n, char + str0 = "", dups(s→l(char + str0))

Rule argument

indvar: str

Additional information

Used simplifier rules: string freely generated by "", +;;