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Proof step 4 from proof val-total (previous step)

∀ str2. str0 = str2 ∨ str0 < str2 ∨ str2 < str0 ⊦ char ' + str0 = str2, char ' + str0 < str2, str2 < char ' + str0

User applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ str0, char. (∀ str2. str0 = str2 ∨ str0 < str2 ∨ str2 < str0) → char ' + str0 = str ∨ char ' + str0 < str ∨ str < char ' + str0, ∀ str2. str0 = str2 ∨ str0 < str2 ∨ str2 < str0 ⊦ char ' + str0 = char0 + str, char ' + str0 < char0 + str, char0 + str < char ' + str0

Rule argument

indvar: str2

Additional information

Used simplifier rules: Less-notempty: ⊦ ¬ str < "";%Less-empty: ⊦ "" < char ' + str;%string freely generated by "", +;;%e-01: ⊦ char ' + str ≠ ""; from specification list[string-new]%a: ⊦ (str + str0) + str1 = str + str0 + str1; from specification list[string-new]