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

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 < char0 ∨ char = char0 ∧ str0 < str ⊦ char ' + str0 < str3

User applied rule case distinction

And obtained the following new goals

Proof step 10:
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
Proof step 14:
char = char0, char0 ' + str < str3, str0 < str, ∀ 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

Rule argument

pos: left 4

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

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information