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Proof step 8 from proof totality (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
key0.ino ≤ ino ⊦ dentrykey(ino, str) = key0, key0 < dentrykey(ino, str), key0.dentry? ∧ ino = key0.ino ∧ str < key0.name, key0.data? ∧ ino = key0.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)