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Proof step 437 from proof inv-rename-dir-dentry (previous step)

dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), err = ESUCCESS, entries0[str0] ≠ ROOT_INO, afs-cons(dirs0, files), afs-cons (dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md ], files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), entries0[str0] ∈ dirs0, str0 ∈ entries0, m ∈ dirs0, asynced2 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (mkinode (m, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]].meta:= md ] [m ] .meta, true, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]].meta:= md ] [m ] .nlink, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]].meta:= md ] [m ] .nsubdirs, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]].meta:= md ] [m ] .size), false ; err, icache); icache_set# (( m ∈ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).meta ] ⊃ mkinode (m, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).meta ] [m ] .meta, true, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).meta ] [m ] .nlink, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).meta ] [m ] .nsubdirs, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).meta ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), false ; err, icache); inode := mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3); ino := entries0[str0]; dirs := dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)]; icache_set# ((entries0[str0] ∈ dirs ⊃ mkinode (entries0[str0], dirs[ino, dirs[ino].meta:= inode.meta][entries0[str0]].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][entries0[str0]].nlink, dirs[ino, dirs[ino].meta:= inode.meta][entries0[str0]].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][entries0[str0]].size) ;mkinode(entries0[str0], files[entries0[str0]].meta, false, files[entries0[str0]].nlink, 0, files[entries0[str0]].size) ), false ; err, icache); dcache_delete# ((m ∈ dirs ⊃ mkinode (m, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).meta, true, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).nlink, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).nsubdirs, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) .ino, mkdentry(str0, entries0[str0]).name ; err, dcache); dcache_set# ((m ∈ dirs ⊃ mkinode (m, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).meta, true, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).nlink, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).nsubdirs, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) .ino, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino).name, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino) ; err, dcache)⟫ ( icache-cons(icache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ dcache-cons(dcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ pcache-cons(pcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ synced(dirs[ino, dirs[ino].meta:= inode.meta], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 438:
dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries0), err = ESUCCESS, mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3) = mkinode(m0, md0, boolvar, m2, m5, m7), afs-cons (dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md ], files), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), m ∈ dirs0, str0 ∈ entries0, entries0[str0] ∈ dirs0, asynced2 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (mkinode (m, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]].meta:= md ] [m ] .meta, true, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]].meta:= md ] [m ] .nlink, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]].meta:= md ] [m ] .nsubdirs, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]].meta:= md ] [m ] .size), false ; err, icache); icache_set# (( m ∈ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]].meta:= md0 ] ⊃ mkinode (m, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]].meta:= md0 ] [m ] .meta, true, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]].meta:= md0 ] [m ] .nlink, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]].meta:= md0 ] [m ] .nsubdirs, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]].meta:= md0 ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), false ; err, icache); inode := mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3); ino := entries0[str0]; dirs := dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)]; icache_set# ((entries0[str0] ∈ dirs ⊃ mkinode (entries0[str0], dirs[ino, dirs[ino].meta:= inode.meta][entries0[str0]].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][entries0[str0]].nlink, dirs[ino, dirs[ino].meta:= inode.meta][entries0[str0]].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][entries0[str0]].size) ;mkinode(entries0[str0], files[entries0[str0]].meta, false, files[entries0[str0]].nlink, 0, files[entries0[str0]].size) ), false ; err, icache); dcache_delete# ((m ∈ dirs ⊃ mkinode (m, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).meta, true, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).nlink, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).nsubdirs, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) .ino, mkdentry(str0, entries0[str0]).name ; err, dcache); dcache_set# ((m ∈ dirs ⊃ mkinode (m, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).meta, true, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).nlink, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).nsubdirs, (m = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m]).size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) .ino, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino).name, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino) ; err, dcache)⟫ ( icache-cons(icache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ dcache-cons(dcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ pcache-cons(pcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ synced(dirs[ino, dirs[ino].meta:= inode.meta], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache))), entries0[str0] = ROOT_INO

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [mkinode (entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3), m0, md0, boolvar, m2, m5, m7]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: mkinode (entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3), m0, md0, boolvar, m2, m5, m7