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Proof step 15 from proof val-trans (previous step)

∀ str0, str, char0. str0 < str ∧ 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) → char0 ' + str0 < str1, str0 < str, char0 ' + str < char + 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 ⊦ char0 ' + str0 < char + str1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
str < str1, str0 < str, ∀ str2, str3. str0 < str2 ∧ str2 < str3 → str0 < str3, ∀ str3, char, str0. str < str3 ∧ char ' + str0 < str ∧ (∀ str2, str3. str0 < str2 ∧ str2 < str3 → str0 < str3) → char ' + str0 < str3, ∀ str0, str, char0. str0 < str ∧ 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) → char0 ' + str0 < str1 ⊦ str0 < str1

Rule argument

Additional information

Used simplifier rules: Less-rec: ⊦ char1 ' + str1 < char2 ' + str2 ↔ char1 < char2 ∨ char1 = char2 ∧ str1 < str2;%Char-irref: ⊦ ¬ char < char;%a: ⊦ (str + str0) + str1 = str + str0 + str1; from specification list[string-new]%c: ⊦ char + str = char ' + str; from specification list[string-new]