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Proof step 6 from proof totality (previous step)

key = datakey(ino, ino0) ⊦ key = key0, key < key0, key0 < key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
key0.ino ≤ ino ⊦ datakey(ino, ino0) = key0, key0 < datakey(ino, ino0), key0.data? ∧ ino = key0.ino ∧ ino0 < key0.part

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%⊦ datakey(ino, n) < key ↔ ino < key.ino ∨ key.data? ∧ ino = key.ino ∧ n < key.part; (ws)