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Proof step 12 from proof transitivity (previous step)

datakey(ino0, ino1) < 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 13:
⊦ datakey(ino, n) < key ↔ ino < key.ino ∨ key.data? ∧ ino = key.ino ∧ n < key.part
Proof step 14:
key1.ino ≤ ino, ino < ino0 ∨ ino = ino0, ino0 < key1.ino ∨ key1.data? ∧ ino0 = key1.ino ∧ ino1 < key1.part ⊦ ¬ key1.inode? ∧ ino = key1.ino

Rule argument

spec: key-order-def name: datakey-less seq: ⊦ datakey(ino, n) < key ↔ ino < key.ino ∨ key.data? ∧ ino = key.ino ∧ n < key.part subst: [key, n, ino] → [key1, ino1, ino0] flags: <all paths>

Additional information

Used terms: key1, ino1, ino0