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Proof step 117 from proof refine-unlink (previous step)

# links(entries[str], cache_dirs) = m0 + 1, cache_files[entries[str]] = mkfile(m2, md3, m0 + 1, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m7, md2, m0 + 1, content0), cache_dirs[m3] = mkdir(m9 + 1, md4, # links(m3, cache_dirs), m8, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dent0 = mkdentry(str, entries[str]), p_inode0 = mkinode(m3, md1, true, # links(m3, cache_dirs), m8, m9 + 1), p_inode1 = mkinode(entries[str], md0, false, m0 + 1, 0, m6), afs-cons(cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m8, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons (cache_dcache -- dentrykey(m3, str), cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m8, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons (cache_icache[entries[str], mkientry(false, mkinode(entries[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m8, m9)) ], cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m8, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m8, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]), pcache-cons(cache_pcache, cache_dirs, cache_files), synced (cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m8, entries -- str)], cache_icache[entries[str], mkientry(false, mkinode(entries[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m8, m9)) ], cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), str ∈ entries, entries[str] ∈ cache_files, m3 ∈ cache_dirs, cache_sync → synced (cache_files[entries[str], mkfile(m6, md0, m0, content)], cache_icache[entries[str], mkientry(false, mkinode(entries[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m8, m9)) ], cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ⟨afs_unlink#(; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs0[m3, mkdir(m9, md1, # links(m3, cache_dirs0), m8, entries -- str)] ∧ afs_files = (cache_files[entries[str], mkfile(m6, md0, m0, content)] ⊕ cache_pcache) ⊕ cache_icache[entries[str], mkientry(false, mkinode(entries[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs0), m8, m9)) ] ∧ (afs_asynced ↔ asynced0) ∧ (m3 ∈ cache_dirs0 ⊃ mkinode(m3, md1, true, # links(m3, cache_dirs0), m8, m9) ;mkinode (m3, (m3 = entries[str] ⊃ mkfile(m6, md0, m0, content);cache_files[m3]).meta, false, (m3 = entries[str] ⊃ mkfile(m6, md0, m0, content);cache_files[m3]).nlink, 0, (m3 = entries[str] ⊃ mkfile(m6, md0, m0, content);cache_files[m3]).size) ) = p_inode0 ∧ (entries[str] ∈ cache_dirs0 ⊃ mkinode (entries[str], (entries[str] = m3 ⊃ mkdir(m9, md1, # links(entries[str], cache_dirs0), m8, entries -- str);cache_dirs0[entries[str]]).meta, true, (entries[str] = m3 ⊃ mkdir(m9, md1, # links(entries[str], cache_dirs0), m8, entries -- str);cache_dirs0[entries[str]]).nlink, (entries[str] = m3 ⊃ mkdir(m9, md1, # links(entries[str], cache_dirs0), m8, entries -- str);cache_dirs0[entries[str]]).nsubdirs, (entries[str] = m3 ⊃ mkdir(m9, md1, # links(entries[str], cache_dirs0), m8, entries -- str);cache_dirs0[entries[str]]).size) ;mkinode(entries[str], md0, false, m0, 0, m6) ) = p_inode1 ∧ negdentry(str) = dent0 ∧ ESUCCESS = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 118:
# links(entries[str], cache_dirs) = m0 + 1, cache_dirs[m3] = mkdir(m9 + 1, md4, # links(m3, cache_dirs), m8, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m7, md2, m0 + 1, content0), cache_files[entries[str]] = mkfile(m2, md3, m0 + 1, content), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = p_inode1, cache_dirs0 = cache_dirs, dent = dent0, dent0 = mkdentry(str, entries[str]), dirs = cache_dirs, err = err0, files = afs_files, p_inode = p_inode0, p_inode0 = mkinode(m3, md1, true, # links(m3, cache_dirs), m8, m9 + 1), p_inode1 = mkinode(entries[str], md0, false, m0 + 1, 0, m6), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m8, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]), dcache-cons(cache_dcache, cache_dirs, cache_files), dcache-cons (cache_dcache -- dentrykey(m3, str), cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m8, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]), icache-cons(cache_icache, cache_dirs, cache_files), icache-cons (cache_icache[entries[str], mkientry(false, mkinode(entries[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m8, m9)) ], cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m8, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]), pcache-cons(cache_pcache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m8, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]), synced(cache_dirs, cache_icache, cache_pcache), synced (cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m8, entries -- str)], cache_icache[entries[str], mkientry(false, mkinode(entries[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m8, m9)) ], cache_pcache), m3 ∈ cache_dirs, entries[str] ∈ cache_files, str ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced (cache_files[entries[str], mkfile(m6, md0, m0, content)], cache_icache[entries[str], mkientry(false, mkinode(entries[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m8, m9)) ], cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ⟨if pre-unlink(p_inode, c_inode, dent, dirs, files) then { let p_ino = p_inode.ino in {dirs[p_ino].entries := dirs[p_ino].entries -- dent.name; dirs[p_ino].size := dirs[p_ino].size - 1; let ino = dent.ino in afs_drop_nlink#(ino; dirs, files); dent := negdentry(dent.name); afs_inode_sync#(p_inode; dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(c_inode.ino, dirs, files); err := ESUCCESS} or fail#(; ; err); asynced := ?} else abort⟩ ( dirs = cache_dirs0[m3, mkdir(m9, md1, # links(m3, cache_dirs0), m8, entries -- str)] ∧ files = (cache_files[entries[str], mkfile(m6, md0, m0, content)] ⊕ cache_pcache) ⊕ cache_icache[entries[str], mkientry(false, mkinode(entries[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs0), m8, m9)) ] ∧ (asynced ↔ asynced0) ∧ (m3 ∈ cache_dirs0 ⊃ mkinode(m3, md1, true, # links(m3, cache_dirs0), m8, m9) ;mkinode (m3, (m3 = entries[str] ⊃ mkfile(m6, md0, m0, content);cache_files[m3]).meta, false, (m3 = entries[str] ⊃ mkfile(m6, md0, m0, content);cache_files[m3]).nlink, 0, (m3 = entries[str] ⊃ mkfile(m6, md0, m0, content);cache_files[m3]).size) ) = p_inode ∧ (entries[str] ∈ cache_dirs0 ⊃ mkinode (entries[str], (entries[str] = m3 ⊃ mkdir(m9, md1, # links(entries[str], cache_dirs0), m8, entries -- str);cache_dirs0[entries[str]]).meta, true, (entries[str] = m3 ⊃ mkdir(m9, md1, # links(entries[str], cache_dirs0), m8, entries -- str);cache_dirs0[entries[str]]).nlink, (entries[str] = m3 ⊃ mkdir(m9, md1, # links(entries[str], cache_dirs0), m8, entries -- str);cache_dirs0[entries[str]]).nsubdirs, (entries[str] = m3 ⊃ mkdir(m9, md1, # links(entries[str], cache_dirs0), m8, entries -- str);cache_dirs0[entries[str]]).size) ;mkinode(entries[str], md0, false, m0, 0, m6) ) = c_inode ∧ negdentry(str) = dent ∧ ESUCCESS = err)

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_unlink#(; P_INODE, C_INODE, DENT, ERR, DIRS, FILES; ASYNCED) {if pre-unlink(P_INODE, C_INODE, DENT, DIRS, FILES) then { let P_INO = P_INODE.ino in {DIRS[P_INO].entries := DIRS[P_INO].entries -- DENT.name; DIRS[P_INO].size := DIRS[P_INO].size - 1; let INO = DENT.ino in afs_drop_nlink#(INO; DIRS, FILES); DENT := negdentry(DENT.name); afs_inode_sync#(P_INODE; DIRS, FILES); afs_inode_sync#(C_INODE; DIRS, FILES); P_INODE := getinode(P_INODE.ino, DIRS, FILES); C_INODE := getinode(C_INODE.ino, DIRS, FILES); ERR := ESUCCESS} or fail#(; ; ERR); ASYNCED := ?} else abort };