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Proof step 35 from proof transitivity (previous step)

key = dentrykey(ino, str), key < key0, key0 < key1 ⊦ key < key1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
key0 < key1, dentrykey(ino, str) < key0, key1.ino ≤ ino ⊦ key1.dentry? ∧ ino = key1.ino ∧ str < key1.name, key1.data? ∧ ino = key1.ino

Rule argument

Additional information

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