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Proof step 150 from proof refine-rename-dir-negdentry (previous step)

(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(m7, md4, # links(entries0[str], cache_dirs), m10, entries1), 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), cache_dirs0[entries0[str]] = mkdir(m3, md8, m17, 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), m10, m7), 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, 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 ⊦ ⟨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)), str0 ∈ entries3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 151:
(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))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base