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Proof step 11 from proof val-trans (previous step)

char < char0, char0 ' + str < char1 ' + str1, ∀ 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, ∀ 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 < char1, char = char1 ∧ str0 < str1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: string-less inst: name: Less-rec seq: ⊦ char1 ' + str1 < char2 ' + str2 ↔ char1 < char2 ∨ char1 = char2 ∧ str1 < str2 subst: [str2, char2, str1, char1] → [str1, char1, str, char0] flags: rewrite, current

Additional information

Used simplifier rules: Char-trans: ⊦ char1 < char2 ∧ char2 < char3 → char1 < char3; Used terms: str1, char1, str, char0