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Proof step 19 from proof transitivity (previous step)

key = datakey(ino, ino0), key < key0, key0 < key1 ⊦ key < key1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
key0 < key1, datakey(ino, ino0) < key0, key1.ino ≤ ino ⊦ key1.data? ∧ ino = key1.ino ∧ ino0 < key1.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)