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Proof step 11 from proof pos-at (previous step)

¬ s→l(str0)[m] ≠ char, m < # str0, ∀ n. n < # str0 → pos(s→l(str0)[n], str0) = n ⊦ pos(s→l(str0)[m], char ' + str0) = m + 1, char ' + str0 = "", str0 = "", char ∈ s→l(str0), dups(s→l(str0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
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))

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + 1 ≠ 0;% ⊦ (str1 + str2) + str3 = str1 + str2 + str3;% ⊦ pos(char, char ' + str) = 0;