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Proof step 112 from proof inv-evict (previous step)

# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), afs-cons(dirs, files), afs-cons(dirs -- m, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced1 → synced(files, icache, pcache) ⊦ m = ROOT_INO, icache-cons(icache -- m, dirs -- m, files)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 113:
⊦ 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 114:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), afs-cons(dirs -- m, files), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced1 → synced(files, icache, pcache) ⊦ m = ROOT_INO, ∀ ino. ino ∈ icache -- m → (icache -- m)[ino].inode.ino = ino ∧ ((icache -- m)[ino].dirty ⊃ valid-file-inode((icache -- m)[ino].inode, dirs -- m, files) ;valid-ino(ino, dirs -- m, files) ∧ valid-inode((icache -- m)[ino].inode, dirs -- m, files) )

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 -- m, dirs -- m, files] flags: <all paths>

Additional information

Used terms: icache -- m, dirs -- m, files