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Proof step 10 from proof val-trans (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 11:
char < char0, char0 ' + str < char1 + str1, ∀ 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, ∀ char0, str, char, str0. char0 ' + str < str1 ∧ char < char0 ∧ (∀ str3, char, str0. str < str3 ∧ char ' + str0 < str ∧ (∀ str2, str3. str2 < str3 ∧ str0 < str2 → str0 < str3) → char ' + str0 < str3) ∧ (∀ str2, str3. str2 < str3 ∧ str0 < str2 → str0 < str3) → char ' + str0 < str1 ⊦ char ' + str0 < char1 + str1

Rule argument

indvar: str3

Additional information

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