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Proof step 106 from proof inv-rename-dir-dentry (previous step)

(m = m0 ⊃ mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0);mkdir(m4, md3, # links(m, dirs0), m7, entries2)) = mkdir(m8, md6, m10, m11, entries1), (entries2[str] = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;(entries2[str] = m0 ⊃ mkdir(m1, md0, # links(entries2[str], dirs0), m2, entries0 -- str0) ;mkdir(m6, md5, # links(entries2[str], dirs0), m9, ∅) ) ) = mkdir(m13, md7, m12 + 1, m15, entries3), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries0), dirs0[m] = mkdir(m4, md3, # links(m, dirs0), m7, entries2), dirs0[entries2[str]] = mkdir(m6, md5, # links(entries2[str], dirs0), m9, ∅), dirs0[entries0[str0]] = mkdir(m3, md4, # links(entries0[str0], dirs0), m5, entries), dirs = dirs0[m, mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])][entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ], entries2[str] ≠ ROOT_INO, afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), str ∈ entries2, m ∈ dirs0, entries0[str0] ∈ dirs0, entries2[str] ∈ dirs0, str0 ∈ entries0, m0 ∈ dirs0, m = m0 → md1 = md2, asynced2 → synced(files, icache, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md1, true, # links(m, dirs0), m7, m4); dirs, files); new_child_inode := mkinode(entries2[str], md, true, # links(entries2[str], dirs0), m9, m6); if true then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := (new_child_inode.ino ∈ dirs ⊃ mkinode (new_child_inode.ino, dirs[new_child_inode.ino].meta, true, dirs[new_child_inode.ino].nlink, dirs[new_child_inode.ino].nsubdirs, dirs[new_child_inode.ino].size) ;mkinode (new_child_inode.ino, files[new_child_inode.ino].meta, false, files[new_child_inode.ino].nlink, 0, files[new_child_inode.ino].size) )}; old_parent_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); new_parent_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); err := ESUCCESS; asynced := ?] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, icache); icache_set#(new_parent_inode, asynced; err, icache); if true then icache_set#(new_child_inode, asynced; err, icache); dcache_delete#(old_parent_inode.ino, mkdentry(str0, entries0[str0]).name; err, dcache); dcache_set# (new_parent_inode.ino, mkdentry(mkdentry(str, entries2[str]).name, mkdentry(str0, entries0[str0]).ino).name, mkdentry(mkdentry(str, entries2[str]).name, mkdentry(str0, entries0[str0]).ino) ; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))), m0 = m ∧ mkdentry(str, entries2[str]) = mkdentry(str0, entries0[str0])

Heuristic unfold applied rule call right

And obtained the following new goals

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_inode_sync#(INODE; DIRS, FILES) {let INO = INODE.ino in if INO ∈ FILES then {FILES[INO].size := INODE.size; FILES[INO].meta := INODE.meta} else if INO ∈ DIRS then DIRS[INO].meta := INODE.meta };