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Proof step 4 from proof transitivity (previous step)

key = inodekey(ino), key < key0, key0 < key1 ⊦ key < key1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
key0 < key1, inodekey(ino) < key0, key1.ino ≤ ino ⊦ ¬ key1.inode? ∧ ino = key1.ino

Rule argument

Additional information

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