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Proof step 3 from proof transitivity (previous step)

key0 < key1, key < key0 ⊦ key < key1

User applied rule constructor cut

And obtained the following new goals

Proof step 4:
key = inodekey(ino), key < key0, key0 < key1 ⊦ key < key1
Proof step 19:
key = datakey(ino, ino0), key < key0, key0 < key1 ⊦ key < key1
Proof step 35:
key = dentrykey(ino, str), key < key0, key0 < key1 ⊦ key < key1

Rule argument

var: key

Additional information

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