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Proof step 1 from proof downcase-A (conclusion)

⊦ downcase('A') = 'a'

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ pos('A', sortedchars) ≤ pos(char, sortedchars) ∧ pos(char, sortedchars) ≤ pos('Z', sortedchars) → downcase(char) = s→l(sortedchars)[pos(char, sortedchars) + (pos('a', sortedchars) - pos('A', sortedchars))]
Proof step 3:
¬(pos('A', sortedchars) ≤ pos('A', sortedchars) ∧ pos('A', sortedchars) ≤ pos('Z', sortedchars)) ⊦ downcase('A') = 'a'
Proof step 8:
pos('A', sortedchars) ≤ pos('A', sortedchars) ∧ pos('A', sortedchars) ≤ pos('Z', sortedchars) ⊦ s→l(sortedchars)[pos('A', sortedchars) + (pos('a', sortedchars) - pos('A', sortedchars))] = 'a'

Rule argument

spec: inst: name: Char-downcase-yes seq: ⊦ pos('A', sortedchars) ≤ pos(char, sortedchars) ∧ pos(char, sortedchars) ≤ pos('Z', sortedchars) → downcase(char) = s→l(sortedchars) [ pos(char, sortedchars) + (pos('a', sortedchars) - pos('A', sortedchars)) ] subst: [char] → ['A'] flags: rewrite, current

Additional information

Used terms: 'A'