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Proof step 209 from proof inv-mkdir (previous step)

dirs[m] = mkdir(m0, md, # links(m, dirs), m2, entries0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, ¬ str ∈ entries0, asynced1 → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪if err = ESUCCESS then let asynced = false in {icache_set#(mkinode(m, md0, true, # links(m, dirs), m2, m0), asynced; err, icache); icache_set#(c_inode, asynced; err, icache); dcache_set#(m, str, negdentry(str); err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 210:
dirs[m] = mkdir(m0, md, # links(m, dirs), m2, entries0), afs-cons(dirs, 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), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [choose err0 with ⌊err0⌋ in err := err0; asynced := ?] ⟪if err = ESUCCESS then let asynced = false in {icache_set#(mkinode(m, md0, true, # links(m, dirs), m2, m0), asynced; err, icache); icache_set#(c_inode, asynced; err, icache); dcache_set#(m, str, negdentry(str); err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache))), str ∈ entries0

Rule argument

pos: right 1

Additional information

Used simplifier rules: fail#(; ; ERR){choose ERR0 with ⌊ERR0⌋ in ERR := ERR0};