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Proof step 151 from proof refine-rename-dir-negdentry (previous step)

(m16 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) = mkdir(m13, md7, m14, m15, entries4), (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md0, # links(m9, cache_dirs), m1, entries0 -- str)) = mkdir(m, md, m11, m12, entries2), (m16 = m9 ⊃ mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str);mkdir(m6, md6, # links(m16, cache_dirs), m8, entries3)) = mkdir(m2, md2, m4, m5, entries), cache_dirs[m9] = mkdir(m0 + 1, md3, # links(m9, cache_dirs), m1 + 1, entries0), cache_dirs[m16] = mkdir(m6, md6, # links(m16, cache_dirs), m8, entries3), cache_dirs[entries0[str]] = mkdir(m3, md8, # links(entries0[str], cache_dirs), m18, entries5), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, new_child_inode1 = new_child_inode0, new_dent0 = negdentry(str0), new_parent_inode0 = mkinode(m16, md5, true, # links(m16, cache_dirs), m8, m6), old_child_inode0 = mkinode(entries0[str], md1, true, # links(entries0[str], cache_dirs), m18, m3), old_dent0 = mkdentry(str, entries0[str]), old_parent_inode0 = mkinode(m9, md0, true, # links(m9, cache_dirs), m1 + 1, m0 + 1), afs-cons (cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), dcache-cons ((cache_dcache -- dentrykey(m9, str))[dentrykey(m16, str0), mkdentry(str0, entries0[str])], cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), icache-cons(cache_icache, cache_dirs, cache_files), icache-cons (cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), synced(cache_dirs, cache_icache, cache_pcache), synced (cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_pcache), m16 ∈ cache_dirs, m9 ∈ cache_dirs, entries0[str] ∈ cache_dirs, str ∈ entries0, ¬ str0 ∈ entries3, m16 = m9 → md5 = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced (cache_files, cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_pcache), links(m16, cache_dirs) ≠ ∅ ∨ m16 = ROOT_INO, links(m9, cache_dirs) ≠ ∅ ∨ m9 = ROOT_INO ⊦ ⟨afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( (m9 ∈ cache_dirs0 ⊃ mkinode (m9, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .meta, true, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .nlink, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .nsubdirs, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .size) ;mkinode(m9, cache_files[m9].meta, false, cache_files[m9].nlink, 0, cache_files[m9].size) ) = old_parent_inode0 ∧ (m16 ∈ cache_dirs0 ⊃ mkinode(m16, md5, true, m14, m15, m13) ;mkinode(m16, cache_files[m16].meta, false, cache_files[m16].nlink, 0, cache_files[m16].size) ) = new_parent_inode0 ∧ mkinode(entries0[str], md1, true, # links(entries0[str], cache_dirs0), m18, m3) = old_child_inode0 ∧ new_child_inode1 = new_child_inode0 ∧ negdentry(str) = old_dent0 ∧ mkdentry(str0, entries0[str]) = new_dent0 ∧ ESUCCESS = err0 ∧ cache_dirs = cache_dirs0 [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs0), m1, entries0 -- str) ) .meta:= md0 ] [m16, (m16 = m9 ∧ m9 ∈ cache_dirs0 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;(m16 ∈ cache_dirs0 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);cache_dirs0[m16]) ) .meta:= md5 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))] [m16, mkientry (false, (m16 ∈ cache_dirs0 ⊃ mkinode(m16, md5, true, m14, m15, m13) ;mkinode(m16, cache_files[m16].meta, false, cache_files[m16].nlink, 0, cache_files[m16].size) )) ] ∧ (afs_asynced ↔ asynced0))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 152:
(m16 = m9 ⊃ mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str);mkdir(m6, md6, # links(m16, cache_dirs), m8, entries3)) = mkdir(m2, md2, m4, m5, entries), (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md0, # links(m9, cache_dirs), m1, entries0 -- str)) = mkdir(m, md, m11, m12, entries2), (m16 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) = mkdir(m13, md7, m14, m15, entries4), cache_dirs[entries0[str]] = mkdir(m3, md8, # links(entries0[str], cache_dirs), m18, entries5), cache_dirs[m16] = mkdir(m6, md6, # links(m16, cache_dirs), m8, entries3), cache_dirs[m9] = mkdir(m0 + 1, md3, # links(m9, cache_dirs), m1 + 1, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dirs = cache_dirs, err = err0, files = afs_files, new_child_inode = new_child_inode0, new_child_inode1 = new_child_inode0, new_dent = new_dent0, new_dent0 = negdentry(str0), new_parent_inode = new_parent_inode0, new_parent_inode0 = mkinode(m16, md5, true, # links(m16, cache_dirs), m8, m6), old_child_inode = old_child_inode0, old_child_inode0 = mkinode(entries0[str], md1, true, # links(entries0[str], cache_dirs), m18, m3), old_dent = old_dent0, old_dent0 = mkdentry(str, entries0[str]), old_parent_inode = old_parent_inode0, old_parent_inode0 = mkinode(m9, md0, true, # links(m9, cache_dirs), m1 + 1, m0 + 1), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons (cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), dcache-cons ((cache_dcache -- dentrykey(m9, str))[dentrykey(m16, str0), mkdentry(str0, entries0[str])], cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons (cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced (cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, # links(m9, cache_dirs), m1, entries0 -- str)) .meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), str ∈ entries0, entries0[str] ∈ cache_dirs, m9 ∈ cache_dirs, m16 ∈ cache_dirs, cache_sync → synced (cache_files, cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), m16 = m9 → md5 = md0, links(m9, cache_dirs) ≠ ∅ ∨ m9 = ROOT_INO, links(m16, cache_dirs) ≠ ∅ ∨ m16 = ROOT_INO ⊦ ⟨if pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) then { let old_ino = old_parent_inode.ino, new_ino = new_parent_inode.ino, asynced1 = new_dent.dentry? in let asynced0 = old_ino = new_ino ∧ new_dent = old_dent in {dirs[old_ino].entries := dirs[old_ino].entries -- old_dent.name; if ¬ asynced0 then {dirs[old_ino].size := dirs[old_ino].size - 1; if old_dent.ino ∈ dirs then dirs[old_ino].nsubdirs := dirs[old_ino].nsubdirs - 1}; dirs[new_ino].entries[new_dent.name] := old_dent.ino; if asynced1 ∧ ¬ asynced0 then let ino = new_dent.ino in afs_drop_nlink#(ino; dirs, files); if ¬ asynced1 then {dirs[new_ino].size := dirs[new_ino].size + 1; if old_dent.ino ∈ dirs then dirs[new_ino].nsubdirs := dirs[new_ino].nsubdirs + 1}; new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(old_parent_inode; dirs, files); afs_inode_sync#(new_parent_inode; dirs, files); if asynced1 then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := getinode(new_child_inode.ino, dirs, files)}; old_parent_inode := getinode(old_parent_inode.ino, dirs, files); new_parent_inode := getinode(new_parent_inode.ino, dirs, files); err := ESUCCESS} or fail#(; ; err); asynced := ?} else abort⟩ ( (m9 ∈ cache_dirs0 ⊃ mkinode (m9, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .meta, true, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .nlink, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .nsubdirs, (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md0, # links(m9, cache_dirs0), m1, entries0 -- str) ) .size) ;mkinode(m9, cache_files[m9].meta, false, cache_files[m9].nlink, 0, cache_files[m9].size) ) = old_parent_inode ∧ (m16 ∈ cache_dirs0 ⊃ mkinode(m16, md5, true, m14, m15, m13) ;mkinode(m16, cache_files[m16].meta, false, cache_files[m16].nlink, 0, cache_files[m16].size) ) = new_parent_inode ∧ mkinode(entries0[str], md1, true, # links(entries0[str], cache_dirs0), m18, m3) = old_child_inode ∧ new_child_inode1 = new_child_inode ∧ negdentry(str) = old_dent ∧ mkdentry(str0, entries0[str]) = new_dent ∧ ESUCCESS = err ∧ dirs = cache_dirs0 [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]) ;mkdir(m0, md3, # links(m9, cache_dirs0), m1, entries0 -- str) ) .meta:= md0 ] [m16, (m16 = m9 ∧ m9 ∈ cache_dirs0 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]) ;(m16 ∈ cache_dirs0 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);cache_dirs0[m16]) ) .meta:= md5 ] ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))] [m16, mkientry (false, (m16 ∈ cache_dirs0 ⊃ mkinode(m16, md5, true, m14, m15, m13) ;mkinode(m16, cache_files[m16].meta, false, cache_files[m16].nlink, 0, cache_files[m16].size) )) ] ∧ (asynced ↔ asynced0)), str0 ∈ entries3

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_rename# (; OLD_PARENT_INODE, NEW_PARENT_INODE, OLD_CHILD_INODE, NEW_CHILD_INODE, OLD_DENT, NEW_DENT, ERR, DIRS, FILES ; ASYNCED ) {if pre-rename (OLD_PARENT_INODE, OLD_DENT, OLD_CHILD_INODE, NEW_PARENT_INODE, NEW_DENT, NEW_CHILD_INODE, DIRS, FILES) then { let OLD_INO = OLD_PARENT_INODE.ino, NEW_INO = NEW_PARENT_INODE.ino, OVERWRITE = NEW_DENT.dentry? in let IDENTITY = OLD_INO = NEW_INO ∧ NEW_DENT = OLD_DENT in {DIRS[OLD_INO].entries := DIRS[OLD_INO].entries -- OLD_DENT.name; if ¬ IDENTITY then {DIRS[OLD_INO].size := DIRS[OLD_INO].size - 1; if OLD_DENT.ino ∈ DIRS then DIRS[OLD_INO].nsubdirs := DIRS[OLD_INO].nsubdirs - 1}; DIRS[NEW_INO].entries[NEW_DENT.name] := OLD_DENT.ino; if OVERWRITE ∧ ¬ IDENTITY then let INO = NEW_DENT.ino in afs_drop_nlink#(INO; DIRS, FILES); if ¬ OVERWRITE then {DIRS[NEW_INO].size := DIRS[NEW_INO].size + 1; if OLD_DENT.ino ∈ DIRS then DIRS[NEW_INO].nsubdirs := DIRS[NEW_INO].nsubdirs + 1}; NEW_DENT := mkdentry(NEW_DENT.name, OLD_DENT.ino); OLD_DENT := negdentry(OLD_DENT.name); afs_inode_sync#(OLD_PARENT_INODE; DIRS, FILES); afs_inode_sync#(NEW_PARENT_INODE; DIRS, FILES); if OVERWRITE then {afs_inode_sync#(NEW_CHILD_INODE; DIRS, FILES); NEW_CHILD_INODE := getinode(NEW_CHILD_INODE.ino, DIRS, FILES)}; OLD_PARENT_INODE := getinode(OLD_PARENT_INODE.ino, DIRS, FILES); NEW_PARENT_INODE := getinode(NEW_PARENT_INODE.ino, DIRS, FILES); ERR := ESUCCESS} or fail#(; ; ERR); ASYNCED := ?} else abort };