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Proof step 23 from proof inv-evict (previous step)

dirs[m] = mkdir(m0, md, m1, m2, entries), err = ESUCCESS, m1 = 0, afs-cons(dirs, files), afs-cons(dirs -- m, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced1 → synced(files, icache, pcache) ⊦ ⟪icache_delete#(m; err, icache); skip⟫ ( icache-cons(icache, dirs -- m, files) ∧ dcache-cons(dcache, dirs -- m, files) ∧ pcache-cons(pcache, dirs -- m, files) ∧ synced(dirs -- m, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache))), m = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), err = ESUCCESS, m ≠ ROOT_INO, afs-cons(dirs, files), afs-cons(dirs -- m, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced1 → synced(files, icache, pcache) ⊦ ⟪icache_delete#(m; err, icache); skip⟫ ( icache-cons(icache, dirs -- m, files) ∧ dcache-cons(dcache, dirs -- m, files) ∧ pcache-cons(pcache, dirs -- m, files) ∧ synced(dirs -- m, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base