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Proof step 397 from proof inv-rename-file-dentry (previous step)

asynced ↔ false, dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), err = ESUCCESS, icache = icache1[inode.ino, mkientry(asynced, inode)], icache1 = icache0[m, mkientry(false, mkinode(m, md2, true, # links(m, dirs0), m4, m1))], inode = mkinode(m, md2, true, # links(m, dirs0), m4, m1), afs-cons(dirs0, files), afs-cons (dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)]), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, asynced2 → synced(files, icache0, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# ((entries[str0] ∈ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)] ⊃ mkinode (entries[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)][entries[str0]].meta, true, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)][entries[str0]].nlink, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)][entries[str0]].nsubdirs, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)][entries[str0]].size) ;mkinode (entries[str0], files [entries[str0], (entries[str0] ∈ files ⊃ files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size ;files[entries[str0]] ) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ] [entries[str0] ] .meta, false, files [entries[str0], (entries[str0] ∈ files ⊃ files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size ;files[entries[str0]] ) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ] [entries[str0] ] .nlink, 0, files [entries[str0], (entries[str0] ∈ files ⊃ files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size ;files[entries[str0]] ) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ] [entries[str0] ] .size) ), false ; err, icache); dcache_delete# ((m ∈ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)] ⊃ mkinode (m, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)][m].meta, true, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)][m].nlink, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)][m].nsubdirs, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)][m].size) ;mkinode (m, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .meta, false, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .nlink, 0, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .size) ) .ino, mkdentry(str0, entries[str0]).name ; err, dcache); dcache_set# ((m ∈ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)] ⊃ mkinode (m, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)][m].meta, true, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)][m].nlink, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)][m].nsubdirs, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)][m].size) ;mkinode (m, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .meta, false, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .nlink, 0, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .size) ) .ino, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files [entries[str0], (entries[str0] ∈ files ⊃ files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size ;files[entries[str0]] ) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ]) ∧ dcache-cons (dcache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files [entries[str0], (entries[str0] ∈ files ⊃ files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size ;files[entries[str0]] ) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ]) ∧ pcache-cons (pcache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files [entries[str0], (entries[str0] ∈ files ⊃ files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size ;files[entries[str0]] ) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ]) ∧ synced(dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], icache, pcache) ∧ ( asynced2 → synced (files [entries[str0], (entries[str0] ∈ files ⊃ files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size ;files[entries[str0]] ) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ], icache, pcache))), entries[str0] ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 398:
dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), err = ESUCCESS, icache = icache0[m, mkientry(false, mkinode(m, md2, true, # links(m, dirs0), m4, m1))], afs-cons(dirs0, files), afs-cons (dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)]), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, ¬ entries[str0] ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (mkinode (entries[str0], files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)][entries[str0]].meta, false, files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)][entries[str0]].nlink, 0, files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)][entries[str0]].size), false ; err, icache); dcache_delete# ((m ∈ dirs0 ⊃ mkinode(m, md2, true, # links(m, dirs0), m4, m1) ;mkinode (m, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .meta, false, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .nlink, 0, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .size) ) .ino, mkdentry(str0, entries[str0]).name ; err, dcache); dcache_set# ((m ∈ dirs0 ⊃ mkinode(m, md2, true, # links(m, dirs0), m4, m1) ;mkinode (m, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .meta, false, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .nlink, 0, (m = entries[str0] ∧ entries[str0] ∈ files ⊃ (files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size) .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ;files[m] ) .size) ) .ino, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ dcache-cons (dcache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ pcache-cons (pcache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], (files[entries[str0]].size:= m2).meta:= md]) ∧ synced(dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], icache, pcache) ∧ (asynced2 → synced(files[entries[str0], (files[entries[str0]].size:= m2).meta:= md], icache, pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ icache[ino, ie][ino, ie0] = icache[ino, ie0]; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)