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Proof step 70 from proof inv-rmdir (previous step)

(entries0[str] = m ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m5, m6, entries), dirs0[m] = mkdir(m0, md1, # links(m, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), dirs = dirs0[entries0[str], mkdir(m3, md2, m5 - 1, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m5 - 1, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ], ino = inode.ino, inode = mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, ino ∈ dirs, 1 ≤ m0, 1 ≤ m2, 1 ≤ m5, asynced1 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [err := ESUCCESS; asynced := ?] ( afs-cons(dirs[ino, dirs[ino].meta:= inode.meta], files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(getinode(entries0[str], dirs[ino, dirs[ino].meta:= inode.meta], files), asynced; err, icache); icache_set# ((m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), asynced ; err, icache); dcache_delete# ((m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) .ino, mkdentry(str, entries0[str]).name ; err, dcache)}⟫ ( icache-cons(icache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ dcache-cons(dcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ pcache-cons(pcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ synced(dirs[ino, dirs[ino].meta:= inode.meta], icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))), entries0[str] = ROOT_INO, m0 = 0, m2 = 0, m5 = 0, ino ∈ files

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 71:
(entries0[str] = m ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m5, m6, entries), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), dirs0[m] = mkdir(m0, md1, # links(m, dirs0), m2, entries0), dirs = dirs0[entries0[str], mkdir(m3, md2, m5 - 1, m6, entries)] [m, (m = entries0[str] ⊃ mkdir(m3, md2, m5 - 1, m6, entries);mkdir(m0 - 1, md1, # links(m, dirs0), m2 - 1, entries0 -- str)).meta:= md ], ino = inode.ino, inode = mkinode(entries0[str], md0, true, # links(entries0[str], dirs0), m4, m1), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), ino ∈ dirs, entries0[str] ∈ dirs0, str ∈ entries0, m ∈ dirs0, 1 ≤ m5, 1 ≤ m2, 1 ≤ m0, asynced1 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [asynced := ?] ( afs-cons(dirs[ino, dirs[ino].meta:= inode.meta], files) → ⟪if ESUCCESS = ESUCCESS then let asynced = false in {err := ESUCCESS; icache_set#(getinode(entries0[str], dirs[ino, dirs[ino].meta:= inode.meta], files), asynced; err, icache); icache_set# ((m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), asynced ; err, icache); dcache_delete# ((m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) .ino, mkdentry(str, entries0[str]).name ; err, dcache)}⟫ ( icache-cons(icache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ dcache-cons(dcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ pcache-cons(pcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ synced(dirs[ino, dirs[ino].meta:= inode.meta], icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))), entries0[str] = ROOT_INO, m0 = 0, m2 = 0, m5 = 0, ino ∈ files

Proof step 70 from proof inv-rmdir (previous step)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

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