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Proof step 9 from proof val-trans (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 10:
∀ char, char0, str, str0. char < char0 ∧ char0 ' + str < str1 ∧ (∀ str3, char, str0. str < str3 ∧ char ' + str0 < str ∧ (∀ str2, str3. str0 < str2 ∧ str2 < str3 → str0 < str3) → char ' + str0 < str3) ∧ (∀ str2, str3. str0 < str2 ∧ str2 < str3 → str0 < str3) → char ' + str0 < str1, char < char0, char0 ' + str < char1 + str1, ∀ str3, char, str0. str < str3 ∧ char ' + str0 < str ∧ (∀ str2, str3. str0 < str2 ∧ str2 < str3 → str0 < str3) → char ' + str0 < str3, ∀ str2, str3. str0 < str2 ∧ str2 < str3 → str0 < str3 ⊦ char ' + str0 < char1 + str1

Rule argument

indvar: str3

Additional information

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