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Proof step 46 from proof transitivity (previous step)

key0 = dentrykey(ino0, str0), key0 < key1, key1.ino ≤ ino, ino < key0.ino ∨ key0.dentry? ∧ ino = key0.ino ∧ str < key0.name ∨ key0.data? ∧ ino = key0.ino ⊦ key1.dentry? ∧ ino = key1.ino ∧ str < key1.name, key1.data? ∧ ino = key1.ino

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
dentrykey(ino0, str0) < key1, key1.ino ≤ ino, ino < ino0 ∨ ino = ino0 ∧ str < str0 ⊦ key1.data? ∧ ino = key1.ino, key1.dentry? ∧ ino = key1.ino ∧ str < key1.name

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ dentrykey(m, str).data?; (s)% ⊦ dentrykey(m, str).name = str; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ dentrykey(m, str).ino = m; (s)