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Proof step 16 from proof transitivity (previous step)

dentrykey(ino0, str) < key1, key1.ino ≤ ino, ino < ino0 ∨ ino = ino0 ⊦ ¬ key1.inode? ∧ ino = key1.ino

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ dentrykey(ino, str) < key ↔ ino < key.ino ∨ key.dentry? ∧ ino = key.ino ∧ str < key.name ∨ key.data? ∧ ino = key.ino
Proof step 18:
key1.ino ≤ ino, ino < ino0 ∨ ino = ino0, ino0 < key1.ino ∨ key1.dentry? ∧ ino0 = key1.ino ∧ str < key1.name ∨ key1.data? ∧ ino0 = key1.ino ⊦ ¬ key1.inode? ∧ ino = key1.ino

Rule argument

spec: key-order-def name: dentrykey-less seq: ⊦ dentrykey(ino, str) < key ↔ ino < key.ino ∨ key.dentry? ∧ ino = key.ino ∧ str < key.name ∨ key.data? ∧ ino = key.ino subst: [key, str, ino] → [key1, str, ino0] flags: <all paths>

Additional information

Used terms: key1, str, ino0