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

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Proof step 139 from proof inv-rename-dir-dentry (previous step)

(entries2[str] = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;(entries2[str] = m0 ⊃ mkdir(m1, md0, # links(entries2[str], dirs0), m2, entries0 -- str0) ;mkdir(m6, md5, # links(entries2[str], dirs0), m9, ∅) ) ) = mkdir(m13, md7, m12 + 1, m15, entries3), (m = m0 ⊃ mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0);mkdir(m4, md3, # links(m, dirs0), m7, entries2)) = mkdir(m8, md6, m10, m11, entries1), dirs0[entries0[str0]] = mkdir(m3, md4, # links(entries0[str0], dirs0), m5, entries), dirs0[entries2[str]] = mkdir(m6, md5, # links(entries2[str], dirs0), m9, ∅), dirs0[m] = mkdir(m4, md3, # links(m, dirs0), m7, entries2), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries0), err = ESUCCESS, icache = icache0 [m0, mkientry (false, mkinode (m0, (m0 = entries2[str] ⊃ (entries2[str] = m ⊃ mkdir(m13, md1, m12, m15, entries3);mkdir(m13, md2, m12, m15, entries3)).meta:= md ;(m0 = m ⊃ mkdir(m8, md1, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md2, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta, true, (m0 = entries2[str] ⊃ (entries2[str] = m ⊃ mkdir(m13, md1, m12, m15, entries3);mkdir(m13, md2, m12, m15, entries3)).meta:= md ;(m0 = m ⊃ mkdir(m8, md1, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md2, # links(m0, dirs0), m2, entries0 -- str0)) ) .nlink, (m0 = entries2[str] ⊃ (entries2[str] = m ⊃ mkdir(m13, md1, m12, m15, entries3);mkdir(m13, md2, m12, m15, entries3)).meta:= md ;(m0 = m ⊃ mkdir(m8, md1, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md2, # links(m0, dirs0), m2, entries0 -- str0)) ) .nsubdirs, (m0 = entries2[str] ⊃ (entries2[str] = m ⊃ mkdir(m13, md1, m12, m15, entries3);mkdir(m13, md2, m12, m15, entries3)).meta:= md ;(m0 = m ⊃ mkdir(m8, md1, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md2, # links(m0, dirs0), m2, entries0 -- str0)) ) .size)) ], entries2[str] ≠ ROOT_INO, afs-cons (dirs0 [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], (entries2[str] = m ⊃ (entries2[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md1 ;(entries2[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)) ) .meta:= md ], 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, str ∈ entries2, m0 ∈ dirs0, str0 ∈ entries0, entries2[str] ∈ dirs0, entries0[str0] ∈ dirs0, asynced2 → synced(files, icache0, pcache), m = m0 → md1 = md2, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪icache_set# (( m ∈ dirs0 [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] ⊃ mkinode (m, dirs0 [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0) ) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) .meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str] ] .meta:= md ] [m ] .meta, true, dirs0 [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0) ) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) .meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str] ] .meta:= md ] [m ] .nlink, dirs0 [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0) ) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) .meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str] ] .meta:= md ] [m ] .nsubdirs, dirs0 [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0) ) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) .meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str] ] .meta:= md ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), false ; err, icache); inode := mkinode(entries2[str], md, true, # links(entries2[str], dirs0), m9, m6); ino := entries2[str]; dirs := dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ]; icache_set# ((entries2[str] ∈ dirs ⊃ mkinode (entries2[str], dirs[ino, dirs[ino].meta:= inode.meta][entries2[str]].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][entries2[str]].nlink, dirs[ino, dirs[ino].meta:= inode.meta][entries2[str]].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][entries2[str]].size) ;mkinode(entries2[str], files[entries2[str]].meta, false, files[entries2[str]].nlink, 0, files[entries2[str]].size) ), false ; err, icache); dcache_delete# ((m0 ∈ dirs ⊃ mkinode (m0, (m0 = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m0]).meta, true, (m0 = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m0]).nlink, (m0 = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m0]).nsubdirs, (m0 = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m0]).size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].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(str, entries2[str]).name, mkdentry(str0, entries0[str0]).ino).name, mkdentry(mkdentry(str, entries2[str]).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))), m0 = m ∧ mkdentry(str, entries2[str]) = mkdentry(str0, entries0[str0])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 140:
(m = m0 ⊃ mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0);mkdir(m4, md3, # links(m, dirs0), m7, entries2)) = mkdir(m8, md6, m10, m11, entries1), (entries2[str] = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;(entries2[str] = m0 ⊃ mkdir(m1, md0, # links(entries2[str], dirs0), m2, entries0 -- str0) ;mkdir(m6, md5, # links(entries2[str], dirs0), m9, ∅) ) ) = mkdir(m13, md7, m12 + 1, m15, entries3), (m0 = entries2[str] ⊃ (entries2[str] = m ⊃ mkdir(m13, md1, m12, m15, entries3);mkdir(m13, md2, m12, m15, entries3)).meta:= md ;(m0 = m ⊃ mkdir(m8, md1, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md2, # links(m0, dirs0), m2, entries0 -- str0)) ) = mkdir(m14, md8, m16, m17, entries4), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries0), dirs0[m] = mkdir(m4, md3, # links(m, dirs0), m7, entries2), dirs0[entries2[str]] = mkdir(m6, md5, # links(entries2[str], dirs0), m9, ∅), dirs0[entries0[str0]] = mkdir(m3, md4, # links(entries0[str0], dirs0), m5, entries), err = ESUCCESS, icache = icache0[m0, mkientry(false, mkinode(m0, md8, true, m16, m17, m14))], afs-cons(dirs0, files), afs-cons (dirs0 [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], (entries2[str] = m ⊃ (entries2[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)).meta:= md1 ;(entries2[str] = m0 ⊃ mkdir(m13, md2, m12, m15, entries3);mkdir(m13, md7, m12, m15, entries3)) ) .meta:= md ], files), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), entries0[str0] ∈ dirs0, entries2[str] ∈ dirs0, str0 ∈ entries0, m0 ∈ dirs0, str ∈ entries2, m ∈ dirs0, m = m0 → md1 = md2, asynced2 → synced(files, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (( m ∈ dirs0 [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] ⊃ mkinode (m, dirs0 [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0) ) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) .meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str] ] .meta:= md ] [m ] .meta, true, dirs0 [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0) ) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) .meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str] ] .meta:= md ] [m ] .nlink, dirs0 [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0) ) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) .meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str] ] .meta:= md ] [m ] .nsubdirs, dirs0 [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str], dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]) ;mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0) ) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) .meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ] [entries2[str] ] .meta:= md ] [m ] .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), false ; err, icache); inode := mkinode(entries2[str], md, true, # links(entries2[str], dirs0), m9, m6); ino := entries2[str]; dirs := dirs0[entries2[str], mkdir(m13, md7, m12, m15, entries3)] [m0, (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3) ;(m0 = m ⊃ mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]]);mkdir(m1, md0, # links(m0, dirs0), m2, entries0 -- str0)) ) .meta:= md2 ] [m, (m = m0 ⊃ (m0 = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])).meta:= md2 ;(m = entries2[str] ⊃ mkdir(m13, md7, m12, m15, entries3);mkdir(m8, md6, m10, m11, entries1[str, entries0[str0]])) ) .meta:= md1 ]; icache_set# ((entries2[str] ∈ dirs ⊃ mkinode (entries2[str], dirs[ino, dirs[ino].meta:= inode.meta][entries2[str]].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][entries2[str]].nlink, dirs[ino, dirs[ino].meta:= inode.meta][entries2[str]].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][entries2[str]].size) ;mkinode(entries2[str], files[entries2[str]].meta, false, files[entries2[str]].nlink, 0, files[entries2[str]].size) ), false ; err, icache); dcache_delete# ((m0 ∈ dirs ⊃ mkinode (m0, (m0 = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m0]).meta, true, (m0 = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m0]).nlink, (m0 = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m0]).nsubdirs, (m0 = ino ∧ ino ∈ dirs ⊃ dirs[ino].meta:= inode.meta;dirs[m0]).size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].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(str, entries2[str]).name, mkdentry(str0, entries0[str0]).ino).name, mkdentry(mkdentry(str, entries2[str]).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))), entries2[str] = ROOT_INO, m0 = m ∧ mkdentry(str, entries2[str]) = mkdentry(str0, entries0[str0])

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [(m0 = entries2[str] ⊃ (entries2[str] = m ⊃ mkdir(m13, md1, m12, m15, entries3) ;mkdir(m13, md2, m12, m15, entries3) ) .meta:= md ;(m0 = m ⊃ mkdir(m8, md1, m10, m11, entries1[str, entries0[str0]]) ;mkdir (m1, md2, # links(m0, dirs0), m2, entries0 -- str0) ) ), m14, md8, m16, m17, entries4]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: (m0 = entries2[str] ⊃ (entries2[str] = m ⊃ mkdir(m13, md1, m12, m15, entries3) ;mkdir(m13, md2, m12, m15, entries3) ) .meta:= md ;(m0 = m ⊃ mkdir(m8, md1, m10, m11, entries1[str, entries0[str0]]) ;mkdir(m1, md2, # links(m0, dirs0), m2, entries0 -- str0) ) ), m14, md8, m16, m17, entries4