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Proof step 388 from proof inv-write_inode (previous step)

afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m ∈ files ⊦ dcache-cons(dcache, dirs, files[m, (files[m].meta:= md).size:= m2]), m ∈ icache

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 389:
⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files))
Proof step 390:
afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), dcache-cons(dcache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ files ⊦ m ∈ icache, ∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files[m, (files[m].meta:= md).size:= m2])

Rule argument

spec: cache-base name: dcache-cons seq: ⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files)) subst: [dcache, dirs, files] → [dcache, dirs, files[m, (files[m].meta:= md).size:= m2]] flags: <all paths>

Additional information

Used terms: dcache, dirs, files[m, (files[m].meta:= md).size:= m2]