[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 98 from proof inv-link (previous step)

dirs0[ino1] = mkdir(m5, md2, # links(ino1, dirs0), m10, entries1), entries[str] = entries2[str], dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m8, entries), entries0[str] = entries2[str], files0[entries2[str]] = mkfile(m0, md6, # links(entries2[str], dirs0), content0), dirs0[m11] = mkdir(m1, md5, # links(m11, dirs0), m9, entries3), dirs0[ino2] = mkdir(m4, md3, # links(ino2, dirs0), m6, entries0), entries1[str] = entries2[str], dirs0[ino3] = mkdir(m7, md4, # links(ino3, dirs0), m12, entries2), dent = mkdentry(str0, mkdentry(str, entries0[str]).ino), err = ESUCCESS, key = dentrykey(p_ino, name), name = mkdentry(str0, mkdentry(str, entries0[str]).ino).name, p_ino = m11, mkdentry(str, entries0[str]).dentry?, afs-cons(dirs0, files0), afs-cons (dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0)]), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), str ∈ entries1, ino1 ∈ dirs0, str ∈ entries, ino0 ∈ dirs0, ino2 ∈ dirs0, str ∈ entries0, ino3 ∈ dirs0, str ∈ entries2, m11 ∈ dirs0, entries2[str] ∈ files0, asynced1 → synced(files0, icache0, pcache), links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(m11, dirs0) ≠ ∅ ∨ m11 = ROOT_INO, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ str0 ∈ entries3, icache-cons (icache0[m11, mkientry(false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1))] [entries2[str], mkientry (false, (entries0[str] ∈ dirs0 ⊃ mkinode (entries0[str], (entries0[str] = m11 ⊃ mkdir(m1 + 1, md0, # links(entries0[str], dirs0), m9, entries3[str0, entries2[str]]);dirs0[entries0[str]]).meta, true, (entries0[str] = m11 ⊃ mkdir(m1 + 1, md0, # links(entries0[str], dirs0), m9, entries3[str0, entries2[str]]);dirs0[entries0[str]]).nlink, (entries0[str] = m11 ⊃ mkdir(m1 + 1, md0, # links(entries0[str], dirs0), m9, entries3[str0, entries2[str]]);dirs0[entries0[str]]) .nsubdirs, (entries0[str] = m11 ⊃ mkdir(m1 + 1, md0, # links(entries0[str], dirs0), m9, entries3[str0, entries2[str]]);dirs0[entries0[str]]).size) ;mkinode (entries0[str], (entries0[str] = entries1[str] ∧ entries1[str] ∈ files0 ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ;mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0) ) .meta, false, (entries0[str] = entries1[str] ∧ entries1[str] ∈ files0 ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ;mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0) ) .nlink, 0, (entries0[str] = entries1[str] ∧ entries1[str] ∈ files0 ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ;mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0) ) .size) )) ], dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ]) ∧ dcache-cons (dcache[key, dent], dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ]) ∧ pcache-cons (pcache, dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ]) ∧ synced (dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], icache0[m11, mkientry(false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1))] [entries2[str], mkientry (false, (entries0[str] ∈ dirs0 ⊃ mkinode (entries0[str], (entries0[str] = m11 ⊃ mkdir(m1 + 1, md0, # links(entries0[str], dirs0), m9, entries3[str0, entries2[str]]);dirs0[entries0[str]]).meta, true, (entries0[str] = m11 ⊃ mkdir(m1 + 1, md0, # links(entries0[str], dirs0), m9, entries3[str0, entries2[str]]);dirs0[entries0[str]]).nlink, (entries0[str] = m11 ⊃ mkdir(m1 + 1, md0, # links(entries0[str], dirs0), m9, entries3[str0, entries2[str]]);dirs0[entries0[str]]) .nsubdirs, (entries0[str] = m11 ⊃ mkdir(m1 + 1, md0, # links(entries0[str], dirs0), m9, entries3[str0, entries2[str]]);dirs0[entries0[str]]).size) ;mkinode (entries0[str], (entries0[str] = entries1[str] ∧ entries1[str] ∈ files0 ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ;mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0) ) .meta, false, (entries0[str] = entries1[str] ∧ entries1[str] ∈ files0 ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ;mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0) ) .nlink, 0, (entries0[str] = entries1[str] ∧ entries1[str] ∈ files0 ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ;mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0) ) .size) )) ], pcache) ∧ ( asynced1 → synced (files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ], icache0[m11, mkientry(false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1))] [entries2[str], mkientry (false, (entries0[str] ∈ dirs0 ⊃ mkinode (entries0[str], (entries0[str] = m11 ⊃ mkdir(m1 + 1, md0, # links(entries0[str], dirs0), m9, entries3[str0, entries2[str]]);dirs0[entries0[str]]) .meta, true, (entries0[str] = m11 ⊃ mkdir(m1 + 1, md0, # links(entries0[str], dirs0), m9, entries3[str0, entries2[str]]);dirs0[entries0[str]]) .nlink, (entries0[str] = m11 ⊃ mkdir(m1 + 1, md0, # links(entries0[str], dirs0), m9, entries3[str0, entries2[str]]);dirs0[entries0[str]]) .nsubdirs, (entries0[str] = m11 ⊃ mkdir(m1 + 1, md0, # links(entries0[str], dirs0), m9, entries3[str0, entries2[str]]);dirs0[entries0[str]]) .size) ;mkinode (entries0[str], (entries0[str] = entries1[str] ∧ entries1[str] ∈ files0 ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ;mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0) ) .meta, false, (entries0[str] = entries1[str] ∧ entries1[str] ∈ files0 ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ;mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0) ) .nlink, 0, (entries0[str] = entries1[str] ∧ entries1[str] ∈ files0 ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ;mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0) ) .size) )) ], pcache))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 99:
dirs0[ino1] = mkdir(m5, md2, # links(ino1, dirs0), m10, entries1), entries[str] = entries2[str], dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m8, entries), entries0[str] = entries2[str], files0[entries2[str]] = mkfile(m0, md6, # links(entries2[str], dirs0), content0), dirs0[m11] = mkdir(m1, md5, # links(m11, dirs0), m9, entries3), dirs0[ino2] = mkdir(m4, md3, # links(ino2, dirs0), m6, entries0), entries1[str] = entries2[str], dirs0[ino3] = mkdir(m7, md4, # links(ino3, dirs0), m12, entries2), afs-cons(dirs0, files0), afs-cons (dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0)]), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), str ∈ entries1, ino1 ∈ dirs0, str ∈ entries, ino0 ∈ dirs0, ino2 ∈ dirs0, str ∈ entries0, ino3 ∈ dirs0, str ∈ entries2, m11 ∈ dirs0, entries2[str] ∈ files0, asynced1 → synced(files0, icache0, pcache), links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(m11, dirs0) ≠ ∅ ∨ m11 = ROOT_INO, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ str0 ∈ entries3, icache-cons (icache0[m11, mkientry(false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1))] [entries2[str], mkientry(false, mkinode(entries2[str], md, false, # links(entries2[str], dirs0) + 1, 0, m15)) ], dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0)]) ∧ dcache-cons (dcache[dentrykey(m11, str0), mkdentry(str0, entries2[str])], dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0)]) ∧ pcache-cons (pcache, dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0)]) ∧ synced (dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], icache0[m11, mkientry(false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1))] [entries2[str], mkientry(false, mkinode(entries2[str], md, false, # links(entries2[str], dirs0) + 1, 0, m15)) ], pcache) ∧ ( asynced1 → synced (files0[entries2[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0)], icache0[m11, mkientry(false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1))] [entries2[str], mkientry(false, mkinode(entries2[str], md, false, # links(entries2[str], dirs0) + 1, 0, m15)) ], pcache))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ mkdentry(str, m).dentry?; (s)