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Proof step 506 from proof refine-rename-dir-dentry (previous step)

(entries0[str0] = m0 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs), m4, entries0) ;mkdir(m10, md6, # links(entries0[str0], cache_dirs), m12, ∅) ) .meta:= md = mkdir(m7, md5, m8, m9, entries1), (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs), m4, entries0) ) = mkdir(m, md1, m2, m5, entries), cache_dirs[entries0[str0]] = mkdir(m10, md6, # links(entries0[str0], cache_dirs), m12, ∅), cache_dirs[m0] = mkdir(m1, md3, # links(m0, cache_dirs), m4, entries0), cache_dirs0[entries0[str0]] = mkdir(m3, md4, m6, m11, entries2), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, new_child_inode0 = mkinode(entries0[str0], md, true, # links(entries0[str0], cache_dirs), m12, m10), new_dent0 = mkdentry(str0, entries0[str0]), new_parent_inode0 = mkinode(m0, md0, true, # links(m0, cache_dirs), m4, m1), old_child_inode0 = mkinode(entries0[str0], md2, true, # links(entries0[str0], cache_dirs), m12, m10), old_dent0 = mkdentry(str0, entries0[str0]), old_parent_inode0 = mkinode(m0, md0, true, # links(m0, cache_dirs), m4, m1), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs[m0, mkdir(m1, md0, # links(m0, cache_dirs), m4, entries0)][entries0[str0], mkdir(m7, md5, m8, m9, entries1)], cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), dcache-cons (cache_dcache[dentrykey(m0, str0), mkdentry(str0, entries0[str0])], cache_dirs[m0, mkdir(m1, md0, # links(m0, cache_dirs), m4, entries0)][entries0[str0], mkdir(m7, md5, m8, m9, entries1)], cache_files), icache-cons(cache_icache, cache_dirs, cache_files), icache-cons (cache_icache[m0, mkientry(false, mkinode(m0, md1, true, m2, m5, m))][entries0[str0], mkientry(false, mkinode(entries0[str0], md5, true, m8, m9, m7))], cache_dirs[m0, mkdir(m1, md0, # links(m0, cache_dirs), m4, entries0)][entries0[str0], mkdir(m7, md5, m8, m9, entries1)], cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m0, mkdir(m1, md0, # links(m0, cache_dirs), m4, entries0)][entries0[str0], mkdir(m7, md5, m8, m9, entries1)], cache_files), synced(cache_dirs, cache_icache, cache_pcache), synced (cache_dirs[m0, mkdir(m1, md0, # links(m0, cache_dirs), m4, entries0)][entries0[str0], mkdir(m7, md5, m8, m9, entries1)], cache_icache[m0, mkientry(false, mkinode(m0, md1, true, m2, m5, m))][entries0[str0], mkientry(false, mkinode(entries0[str0], md5, true, m8, m9, m7))], cache_pcache), str0 ∈ entries0, entries0[str0] ∈ cache_dirs, m0 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced (cache_files, cache_icache[m0, mkientry(false, mkinode(m0, md1, true, m2, m5, m))] [entries0[str0], mkientry(false, mkinode(entries0[str0], md5, true, m8, m9, m7)) ], cache_pcache), links(m0, cache_dirs) ≠ ∅ ∨ m0 = 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)⟩ ( (m0 ∈ cache_dirs0 ⊃ mkinode (m0, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .meta, true, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .nlink, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .nsubdirs, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .size) ;mkinode(m0, cache_files[m0].meta, false, cache_files[m0].nlink, 0, cache_files[m0].size) ) = old_parent_inode0 ∧ (m0 ∈ cache_dirs0 ⊃ mkinode (m0, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .meta, true, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .nlink, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .nsubdirs, (m0 = entries0[str0] ⊃ mkdir(m1, md, # links(entries0[str0], cache_dirs0), m4, entries0) ;mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0) ) .size) ;mkinode(m0, cache_files[m0].meta, false, cache_files[m0].nlink, 0, cache_files[m0].size) ) = new_parent_inode0 ∧ mkinode(entries0[str0], md2, true, # links(entries0[str0], cache_dirs0), m11, m3) = old_child_inode0 ∧ (entries0[str0] ∈ cache_dirs0 ⊃ mkinode (entries0[str0], md, true, (entries0[str0] = m0 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs0), m4, entries0);cache_dirs0[entries0[str0]]).nlink, (entries0[str0] = m0 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs0), m4, entries0);cache_dirs0[entries0[str0]]).nsubdirs, (entries0[str0] = m0 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs0), m4, entries0);cache_dirs0[entries0[str0]]).size) ;mkinode(entries0[str0], cache_files[entries0[str0]].meta, false, cache_files[entries0[str0]].nlink, 0, cache_files[entries0[str0]].size) ) = new_child_inode0 ∧ negdentry(str0) = old_dent0 ∧ mkdentry(str0, entries0[str0]) = new_dent0 ∧ ESUCCESS = err0 ∧ cache_dirs = cache_dirs0[m0, mkdir(m1, md0, # links(m0, cache_dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m0 ∧ entries0[str0] ∈ cache_dirs0 ⊃ mkdir(m1, md0, # links(entries0[str0], cache_dirs0), m4, entries0) ;cache_dirs0[entries0[str0]] ) .meta:= md ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m0, mkientry(false, mkinode(m0, md1, true, m2, m5, m))] [entries0[str0], mkientry(false, mkinode(entries0[str0], md5, true, m8, m9, m7)) ] ∧ (afs_asynced ↔ asynced0)), entries0[str0] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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