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Proof step 12 from proof val-total (previous step)

char = char0, ∀ str2. str0 = str2 ∨ str2 < str0 ∨ str0 < str2, ∀ str0, char. (∀ str2. str0 = str2 ∨ str2 < str0 ∨ str0 < str2) → char ' + str0 = str ∨ str < char ' + str0 ∨ char ' + str0 < str ⊦ char < char0, char0 < char, char = char0 ∧ str0 = str, char = char0 ∧ str0 < str, char0 = char ∧ str < str0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
∀ str0, char. (∀ str2. str0 = str2 ∨ str2 < str0 ∨ str0 < str2) → char ' + str0 = str ∨ str < char ' + str0 ∨ char ' + str0 < str, ∀ str2. str0 = str2 ∨ str2 < str0 ∨ str0 < str2 ⊦ str0 = str, str < str0, str0 < str

Rule argument

Additional information

Used simplifier rules: Char-irref: ⊦ ¬ char < char;