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Proof step 70 from proof refine-link (previous step)

asynced ↔ false, cache_dirs[ino2] = mkdir(m7, md5, # links(ino2, cache_dirs), m11, entries1), entries[str] = entries1[str], cache_files[entries1[str]] = mkfile(m3, md6, # links(entries1[str], cache_dirs), content1), entries0[str] = entries1[str], cache_dirs[m] = mkdir(m1, md4, # links(m, cache_dirs), m8, entries2), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str]] = mkfile(m5, md1, # links(entries1[str], cache_dirs), content), cache_dirs[ino1] = mkdir(m0, md3, # links(ino1, cache_dirs), m2, entries0), cache_dirs[ino0] = mkdir(m4, md2, # links(ino0, cache_dirs), m10, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = getinode (mkdentry(str, entries0[str]).ino, dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]), dirs = cache_dirs[m, mkdir(m1 + 1, md, # links(m, cache_dirs), m8, entries2[str0, entries1[str]])], err = ESUCCESS, files = cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)], ino = inode.ino, inode = mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6), new_dent = mkdentry(str0, mkdentry(str, entries0[str]).ino), p_inode = (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].meta, false, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].nlink, 0, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].size) ), mkdentry(str, entries0[str]).dentry?, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), str ∈ entries0, ino ∈ files, m ∈ cache_dirs, str ∈ entries1, ino2 ∈ cache_dirs, str ∈ entries, ino0 ∈ cache_dirs, ino1 ∈ cache_dirs, entries1[str] ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(ino2, cache_dirs) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino0, cache_dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, cache_dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set#(p_inode, asynced; err, cache_icache); icache_set#(c_inode, asynced; err, cache_icache); dcache_set#(p_inode.ino, new_dent.name, new_dent; err, cache_dcache)⟫ ⟨old_dent0 := negdentry(str0); p_inode0 := mkinode(m, md, true, # links(m, cache_dirs), m8, m1); p_inode1 := mkinode(entries0[str], md0, false, # links(entries[str], cache_dirs), 0, m6); afs_link#(mkdentry(str, entries0[str]); p_inode0, p_inode1, old_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = dirs ∧ afs_files = (files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta] ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ new_dent = old_dent0 ∧ err = err0), str0 ∈ entries2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 71:
cache_dirs[ino0] = mkdir(m4, md2, # links(ino0, cache_dirs), m10, entries), cache_dirs[ino1] = mkdir(m0, md3, # links(ino1, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str]] = mkfile(m5, md1, # links(entries1[str], cache_dirs), content), cache_dirs[m] = mkdir(m1, md4, # links(m, cache_dirs), m8, entries2), entries0[str] = entries1[str], cache_files[entries1[str]] = mkfile(m3, md6, # links(entries1[str], cache_dirs), content1), entries[str] = entries1[str], cache_dirs[ino2] = mkdir(m7, md5, # links(ino2, cache_dirs), m11, entries1), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), str ∈ entries0, ino1 ∈ cache_dirs, ino0 ∈ cache_dirs, str ∈ entries, ino2 ∈ cache_dirs, str ∈ entries1, m ∈ cache_dirs, entries1[str] ∈ cache_files, ¬ str0 ∈ entries2, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino1, cache_dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, cache_dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino2, cache_dirs) ≠ ∅ ∨ ino2 = ROOT_INO ⊦ ⟪icache_set# (mkinode (m, cache_dirs[m, mkdir(m1 + 1, md, # links(m, cache_dirs), m8, entries2[str0, entries1[str]])][m].meta, true, cache_dirs[m, mkdir(m1 + 1, md, # links(m, cache_dirs), m8, entries2[str0, entries1[str]])][m].nlink, cache_dirs[m, mkdir(m1 + 1, md, # links(m, cache_dirs), m8, entries2[str0, entries1[str]])][m].nsubdirs, cache_dirs[m, mkdir(m1 + 1, md, # links(m, cache_dirs), m8, entries2[str0, entries1[str]])][m].size), false ; err, cache_icache); icache_set# (getinode (mkdentry(str, entries0[str]).ino, cache_dirs[m, mkdir(m1 + 1, md, # links(m, cache_dirs), m8, entries2[str0, entries1[str]])], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)] [entries[str], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)] [entries[str], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)][entries[str]] .size:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).size ] [entries[str] ] .meta:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).meta ]), false ; err, cache_icache); dcache_set# ((m ∈ cache_dirs[m, mkdir(m1 + 1, md, # links(m, cache_dirs), m8, entries2[str0, entries1[str]])] ⊃ mkinode (m, cache_dirs[m, mkdir(m1 + 1, md, # links(m, cache_dirs), m8, entries2[str0, entries1[str]])][m].meta, true, cache_dirs[m, mkdir(m1 + 1, md, # links(m, cache_dirs), m8, entries2[str0, entries1[str]])][m].nlink, cache_dirs[m, mkdir(m1 + 1, md, # links(m, cache_dirs), m8, entries2[str0, entries1[str]])][m].nsubdirs, cache_dirs[m, mkdir(m1 + 1, md, # links(m, cache_dirs), m8, entries2[str0, entries1[str]])][m].size) ;mkinode (m, cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)] [entries[str], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)] [entries[str], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)][entries[str]] .size:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).size ] [entries[str] ] .meta:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).meta ] [m ] .meta, false, cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)] [entries[str], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)] [entries[str], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)][entries[str]] .size:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).size ] [entries[str] ] .meta:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).meta ] [m ] .nlink, 0, cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)] [entries[str], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)] [entries[str], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)][entries[str]] .size:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).size ] [entries[str] ] .meta:= mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6).meta ] [m ] .size) ) .ino, mkdentry(str0, mkdentry(str, entries0[str]).ino).name, mkdentry(str0, mkdentry(str, entries0[str]).ino) ; err, cache_dcache)⟫ ⟨old_dent0 := negdentry(str0); p_inode0 := mkinode(m, md, true, # links(m, cache_dirs), m8, m1); p_inode1 := mkinode(entries0[str], md0, false, # links(entries[str], cache_dirs), 0, m6); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; cache_dirs4 := cache_dirs; afs_link#(mkdentry(str, entries0[str]); p_inode0, p_inode1, old_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs3[m, mkdir(m1 + 1, md, # links(m, cache_dirs3), m8, entries2[str0, entries1[str]])] ∧ afs_files = ( cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs2) + 1, content1)] [entries[str], mkfile(m6, md0, # links(entries1[str], cache_dirs2) + 1, content1) ] ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ (m ∈ cache_dirs3 ⊃ mkinode(m, md, true, # links(m, cache_dirs3), m8, m1 + 1) ;mkinode (m, (m = entries[str] ⊃ mkfile(m6, md0, # links(entries1[str], cache_dirs2) + 1, content1);cache_files[m]).meta, false, (m = entries[str] ⊃ mkfile(m6, md0, # links(entries1[str], cache_dirs2) + 1, content1);cache_files[m]).nlink, 0, (m = entries[str] ⊃ mkfile(m6, md0, # links(entries1[str], cache_dirs2) + 1, content1);cache_files[m]).size) ) = p_inode0 ∧ (entries0[str] ∈ cache_dirs4 ⊃ mkinode (entries0[str], (entries0[str] = m ⊃ mkdir(m1 + 1, md, # links(entries0[str], cache_dirs4), m8, entries2[str0, entries1[str]]) ;cache_dirs4[entries0[str]] ) .meta, true, (entries0[str] = m ⊃ mkdir(m1 + 1, md, # links(entries0[str], cache_dirs4), m8, entries2[str0, entries1[str]]) ;cache_dirs4[entries0[str]] ) .nlink, (entries0[str] = m ⊃ mkdir(m1 + 1, md, # links(entries0[str], cache_dirs4), m8, entries2[str0, entries1[str]]) ;cache_dirs4[entries0[str]] ) .nsubdirs, (entries0[str] = m ⊃ mkdir(m1 + 1, md, # links(entries0[str], cache_dirs4), m8, entries2[str0, entries1[str]]) ;cache_dirs4[entries0[str]] ) .size) ;mkinode (entries0[str], (entries0[str] = entries[str] ⊃ mkfile(m6, md0, # links(entries1[str], cache_dirs4) + 1, content1) ;mkfile(m3, md6, # links(entries1[str], cache_dirs4) + 1, content1) ) .meta, false, (entries0[str] = entries[str] ⊃ mkfile(m6, md0, # links(entries1[str], cache_dirs4) + 1, content1) ;mkfile(m3, md6, # links(entries1[str], cache_dirs4) + 1, content1) ) .nlink, 0, (entries0[str] = entries[str] ⊃ mkfile(m6, md0, # links(entries1[str], cache_dirs4) + 1, content1) ;mkfile(m3, md6, # links(entries1[str], cache_dirs4) + 1, content1) ) .size) ) = p_inode1 ∧ mkdentry(str0, entries0[str]) = old_dent0 ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)