[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 125 from proof refine-mkdir (previous step)

(abs-dirs(fs1, ri1)[m0, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(m0, fs1, ri1)[str, n])] ++ n)[m0] = mkdir(m, md0, m3, m4, entries), fs1[ri1[inodekey(m0)]] = inodenode(key0, md1, true, m1, m2, m6), fo.inodes?, orphans(fs1, ri1).inodes?, afs-cons ((abs-dirs(fs1, ri1)[m0, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(m0, fs1, ri1)[str, n])] ++ n)[n, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m3, m4, entries) ], abs-files(fs1, ri1)), afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), file-node-cons(fs1, ri1), file-node-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), log-cons(log0, fs1), log-cons (log0, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ]), orphans-cons(fs1, ri1, orphans(fs1, ri1)), orphans-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1)), replay-cons-strong(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), replay-cons-strong (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri1), ri-inj(ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), ubifs-cons(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ubifs-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri1[inodekey(m0)] ∈ fs1, inodekey(m0) ∈ ri1, asynced0 → boolvar0, m1 ≠ 0 ∨ m0 = ROOT_INO, links(m0, abs-dirs(fs1, ri1)) ≠ ∅ ∨ m0 = ROOT_INO ⊦ (abs-dirs(fs1, ri1)[m0, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(m0, fs1, ri1)[str, n])] ++ n)[n, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m3, m4, entries) ] = abs-dirs (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, n = 0, dentrykey(m0, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, m1 = 0 ∧ m0 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 126:
(abs-dirs(fs1, ri1)[m0, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(m0, fs1, ri1)[str, n])] ++ n)[m0] = mkdir(m, md0, m3, m4, entries), fs1[ri1[inodekey(m0)]] = inodenode(key0, md1, true, m1, m2, m6), fo.inodes?, orphans(fs1, ri1).inodes?, afs-cons ((abs-dirs(fs1, ri1)[m0, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(m0, fs1, ri1)[str, n])] ++ n)[n, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m3, m4, entries) ], abs-files(fs1, ri1)), afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), file-node-cons(fs1, ri1), file-node-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), log-cons(log0, fs1), log-cons (log0, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ]), orphans-cons(fs1, ri1, orphans(fs1, ri1)), orphans-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1)), replay-cons-strong(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), replay-cons-strong (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri1), ri-inj(ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), ubifs-cons(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ubifs-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri1[inodekey(m0)] ∈ fs1, inodekey(m0) ∈ ri1, asynced0 → boolvar0, m1 ≠ 0 ∨ m0 = ROOT_INO, links(m0, abs-dirs(fs1, ri1)) ≠ ∅ ∨ m0 = ROOT_INO ⊦ adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, n = 0, dentrykey(m0, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, m1 = 0 ∧ m0 ≠ ROOT_INO, ( ino = n ∨ inodekey(ino) ∈ ri1 ∧ fs1[ri1[inodekey(ino)]].directory ↔ inodekey(ino) ∈ ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3] ∧ (adr3 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1) ;fs1[(n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)]))] ) ) ) .directory) ∧ ( ino = n ∨ inodekey(ino) ∈ ri1 ∧ fs1[ri1[inodekey(ino)]].directory → (ino = m0 ⊃ mkdir(m, md2, m3, m4, entries) ;(ino = n ⊃ mkdir(0, md, 1, 0, ∅);(abs-dirs(fs1, ri1)[m0, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(m0, fs1, ri1)[str, n])] ++ n)[ino]) ) = mkdir ((adr3 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1) ;fs1[(n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)]))] ) ) ) .size, (adr3 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1) ;fs1[(n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)]))] ) ) ) .meta, (adr3 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1) ;fs1[(n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)]))] ) ) ) .nlink, (adr3 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1) ;fs1[(n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)]))] ) ) ) .nsubdirs, abs-children (ino, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3])))

Rule argument

Additional information

Used simplifier rules: at-ri: ⊦ ri[key, adr][key0] = (key = key0 ⊃ adr;ri[key0]);% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)%ino ≠ 0, ¬ ino ∈ dirs ⊦ ino0 ∈ dirs ++ ino ↔ ino0 = ino ∨ ino0 ∈ dirs; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)%⊦ dirs = abs-dirs(fs, ri) ↔ (∀ ino. ( ino ∈ dirs ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory) ∧ (ino ∈ dirs → dirs[ino] = abs-dir(ino, fs, ri))); (ss)