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Proof step 20 from proof transitivity (previous step)

key0 < key1, datakey(ino, ino0) < key0, key1.ino ≤ ino ⊦ key1.data? ∧ ino = key1.ino ∧ ino0 < key1.part

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ datakey(ino, n) < key ↔ ino < key.ino ∨ key.data? ∧ ino = key.ino ∧ n < key.part
Proof step 22:
key0 < key1, key1.ino ≤ ino, ino < key0.ino ∨ key0.data? ∧ ino = key0.ino ∧ ino0 < key0.part ⊦ key1.data? ∧ ino = key1.ino ∧ ino0 < key1.part

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] → [key0, ino0, ino] flags: <all paths>

Additional information

Used terms: key0, ino0, ino