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Proof step 5 from proof val-trans (previous step)

str2 < str3, char ' + str0 < str2, ∀ str2, str3. str2 < str3 ∧ str0 < str2 → str0 < str3 ⊦ char ' + str0 < str3

User applied rule structural induction

And obtained the following new goals

Proof step 6:
char ' + str0 < char0 + str, char0 + str < str3, ∀ str2, str3. str2 < str3 ∧ str0 < str2 → str0 < str3, ∀ str3, char, str0. str < str3 ∧ char ' + str0 < str ∧ (∀ str2, str3. str2 < str3 ∧ str0 < str2 → str0 < str3) → char ' + str0 < str3 ⊦ char ' + str0 < str3

Rule argument

indvar: str2

Additional information

Used simplifier rules: less-empty: ⊦ "" < str ↔ str ≠ "";%Less-notempty: ⊦ ¬ str < "";%string freely generated by "", +;;