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Proof step 450 from proof inv-rename-dir-dentry (previous step)

(m = entries0[str0] ⊃ mkdir(m1, md0, # links(entries0[str0], dirs0), m4, entries0);mkdir(m1, md2, # links(m, dirs0), m4, entries0)) = mkdir(m0, md, m2, m5, entries), dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), err = ESUCCESS, icache = icache0[m, mkientry(false, mkinode(m, md, true, m2, m5, m0))], 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:= md0 ], files), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), entries0[str0] ∈ dirs0, str0 ∈ entries0, m ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (mkinode (entries0[str0], 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 ] [entries0[str0] ] .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 ] [entries0[str0] ] .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 ] [entries0[str0] ] .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 ] [entries0[str0] ] .size), false ; err, icache); dcache_delete# ((m ∈ dirs0 ⊃ mkinode (m, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3).meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .meta, true, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3).meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .nlink, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3).meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .nsubdirs, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3).meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .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 ∈ dirs0 ⊃ mkinode (m, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3).meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .meta, true, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3).meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .nlink, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3).meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .nsubdirs, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3).meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .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, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ dcache-cons (dcache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ pcache-cons (pcache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ synced (dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 451:
(m = entries0[str0] ⊃ mkdir(m1, md0, # links(entries0[str0], dirs0), m4, entries0);mkdir(m1, md2, # links(m, dirs0), m4, entries0)) = mkdir(m0, md, m2, m5, entries), (m ∈ dirs0 ⊃ mkinode (m, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3).meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .meta, true, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3).meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .nlink, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3).meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .nsubdirs, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0]] .meta:= mkinode(entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3).meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) = mkinode(m7, md4, boolvar, m8, m9, m10), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries0), err = ESUCCESS, icache = icache0[m, mkientry(false, mkinode(m, md, true, m2, m5, m0))], 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:= md0 ], files), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m ∈ dirs0, str0 ∈ entries0, entries0[str0] ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (mkinode (entries0[str0], 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 ] [entries0[str0] ] .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 ] [entries0[str0] ] .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 ] [entries0[str0] ] .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 ] [entries0[str0] ] .size), false ; err, icache); dcache_delete#(m7, mkdentry(str0, entries0[str0]).name; err, dcache); dcache_set# (m7, 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, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ dcache-cons (dcache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ pcache-cons (pcache, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ synced (dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], 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] → [(m ∈ dirs0 ⊃ mkinode (m, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0 [m, mkdir (m1, md2, # links(m, dirs0), m4, entries0) ] [entries0[str0] ] .meta:= mkinode (entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3) .meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .meta, true, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0 [m, mkdir (m1, md2, # links(m, dirs0), m4, entries0) ] [entries0[str0] ] .meta:= mkinode (entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3) .meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .nlink, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0 [m, mkdir (m1, md2, # links(m, dirs0), m4, entries0) ] [entries0[str0] ] .meta:= mkinode (entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3) .meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .nsubdirs, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0 [m, mkdir (m1, md2, # links(m, dirs0), m4, entries0) ] [entries0[str0] ] .meta:= mkinode (entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3) .meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .size) ;mkinode (m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), m7, md4, boolvar, m8, m9, m10]

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: (m ∈ dirs0 ⊃ mkinode (m, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0] ] .meta:= mkinode (entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3) .meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .meta, true, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0] ] .meta:= mkinode (entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3) .meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .nlink, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0] ] .meta:= mkinode (entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3) .meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .nsubdirs, (m = entries0[str0] ∧ entries0[str0] ∈ dirs0 ⊃ dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0] ] .meta:= mkinode (entries0[str0], md0, true, # links(entries0[str0], dirs0), m6, m3) .meta ;mkdir(m1, md2, # links(m, dirs0), m4, entries0) ) .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), m7, md4, boolvar, m8, m9, m10