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Proof step 5 from proof transitivity (previous step)

key0 < key1, inodekey(ino) < key0, key1.ino ≤ ino ⊦ ¬ key1.inode? ∧ ino = key1.ino

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ inodekey(ino) < key ↔ ino < key.ino ∨ ¬ key.inode? ∧ ino = key.ino
Proof step 7:
key0 < key1, key1.ino ≤ ino, ino < key0.ino ∨ ¬ key0.inode? ∧ ino = key0.ino ⊦ ¬ key1.inode? ∧ ino = key1.ino

Rule argument

spec: key-order-def name: inode-less seq: ⊦ inodekey(ino) < key ↔ ino < key.ino ∨ ¬ key.inode? ∧ ino = key.ino subst: [key, ino] → [key0, ino] flags: <all paths>

Additional information

Used terms: key0, ino