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Proof step 36 from proof transitivity (previous step)

key0 < key1, dentrykey(ino, str) < key0, key1.ino ≤ ino ⊦ key1.dentry? ∧ ino = key1.ino ∧ str < key1.name, key1.data? ∧ ino = key1.ino

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ dentrykey(ino, str) < key ↔ ino < key.ino ∨ key.dentry? ∧ ino = key.ino ∧ str < key.name ∨ key.data? ∧ ino = key.ino
Proof step 38:
key0 < key1, key1.ino ≤ ino, ino < key0.ino ∨ key0.dentry? ∧ ino = key0.ino ∧ str < key0.name ∨ key0.data? ∧ ino = key0.ino ⊦ key1.data? ∧ ino = key1.ino, key1.dentry? ∧ ino = key1.ino ∧ str < key1.name

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

Additional information

Used terms: key0, str, ino