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Proof step 38 from proof transitivity (previous step)

key0 < key1, key1.ino ≤ ino, ino < key0.ino ∨ key0.dentry? ∧ ino = key0.ino ∧ str < key0.name ∨ key0.data? ∧ ino = key0.ino ⊦ key1.data? ∧ ino = key1.ino, key1.dentry? ∧ ino = key1.ino ∧ str < key1.name

User applied rule constructor cut

And obtained the following new goals

Proof step 39:
key0 = inodekey(ino0), 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
Proof step 42:
key0 = datakey(ino0, ino1), 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
Proof step 46:
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

Rule argument

var: key0

Additional information

Used simplifier rules: key freely generated by inodekey, datakey, dentrykey;;