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Proof step 399 from proof inv-write_inode (previous step)

afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), icache-cons(icache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ files ⊦ icache-cons(icache, 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 400:
⊦ icache-cons(icache, dirs, files) ↔ (∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files) ;valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files) ))
Proof step 401:
afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m ∈ files ⊦ m ∈ icache, ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files[m, (files[m].meta:= md).size:= m2]) ; valid-ino(ino, dirs, files[m, (files[m].meta:= md).size:= m2]) ∧ valid-inode(icache[ino].inode, dirs, files[m, (files[m].meta:= md).size:= m2]) )

Rule argument

spec: cache-base name: icache-cons seq: ⊦ icache-cons(icache, dirs, files) ↔ (∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files) ; valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files) )) subst: [icache, dirs, files] → [icache, dirs, files[m, (files[m].meta:= md).size:= m2]] flags: <all paths>

Additional information

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