[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

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

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

User applied rule insert lemma

And obtained the following new goals

Proof step 11:
⊦ char1 < char2 ∨ char1 = char2 ∨ char2 < char1
Proof step 12:
char = char0, ∀ str2. str0 = str2 ∨ str2 < str0 ∨ str0 < str2, ∀ str0, char. (∀ str2. str0 = str2 ∨ str2 < str0 ∨ str0 < str2) → char ' + str0 = str ∨ str < char ' + str0 ∨ char ' + str0 < str ⊦ char < char0, char0 < char, char = char0 ∧ str0 = str, char = char0 ∧ str0 < str, char0 = char ∧ str < str0

Rule argument

spec: <toplevel> name: Char-total seq: ⊦ char1 < char2 ∨ char1 = char2 ∨ char2 < char1 subst: [char1, char2] → [char, char0]

Additional information

Used terms: char, char0