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Proof step 6 from proof downcase-lower-a (previous step)

28 ≤ pos('a', sortedchars), pos('a', sortedchars) ≤ pos('Z', sortedchars), 28 ≤ pos('Z', sortedchars) ⊦ downcase('a') = 'a'

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
28 ≤ pos('a', sortedchars), pos('a', sortedchars) ≤ pos('Z', sortedchars), 28 ≤ pos('Z', sortedchars) ⊦ downcase('a') = 'a', pos('a', sortedchars) = 0, pos('Z', sortedchars) = 0

Rule argument

Additional information

Used simplifier rules: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)%0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward)