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Proof step 4 from proof totality (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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