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Proof step 12 from proof pos-at (previous step)

m < # str0, ∀ n. n < # str0 → pos(s→l(str0)[n], str0) = n ⊦ s→l(str0)[m] ' + str0 = "", str0 = "", s→l(str0)[m] ∈ s→l(str0), dups(s→l(str0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ m < # chars → (¬ chars[m] ∈ chars ↔ false)

Rule argument

spec: list-del inst: charlist name: get-in seq: ⊦ m < # chars → (¬ chars[m] ∈ chars ↔ false) subst: [m, chars] → [m, s→l(str0)] flags: rewrite

Additional information

Used simplifier rules: s2l-length: ⊦ # s→l(str) = # str;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n → (n ≤ m ↔ false); Used terms: m, s→l(str0)