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Proof step 1 from proof downcase-rec (conclusion)

⊦ str ≠ "" → downcase(str) = downcase(str.char1) + downcase(str.rstring)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ str = "", downcase(str) = downcase(str.char1) ' + downcase(str.rstring)

Rule argument

Additional information

Used simplifier rules: ⊦ char + str = char ' + str;