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Proof step 166 from proof refine-create (previous step)

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, md2, m1, m2, abs-children(m0, fs1, ri1)[str, n])], (abs-files(fs1, ri1) ++ n)[n, mkfile(0, md, 1, ∅)]), 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, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 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, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ]), orphans-cons(fs1, ri1, orphans(fs1, ri1)), orphans-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 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, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 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, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 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, false, 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, m6 + 1) ;fs1[(n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)]))] ) ) ) .directory) ∧ ( ino = n ∨ inodekey(ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(ino)]].directory → (ino = n ⊃ mkfile(0, md, 1, ∅);(abs-files(fs1, ri1) ++ n)[ino]) = mkfile ((adr3 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ inodenode(inodekey(n), md, false, 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, 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, false, 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, 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, false, 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, m6 + 1) ;fs1[(n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)]))] ) ) ) .nlink, abs-content (ino, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3])))

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 167:
fs1[ri1[inodekey(m0)]] = inodenode(key0, md1, true, m1, m2, m6), orphans(fs1, ri1).inodes?, fo.inodes?, afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), afs-cons(abs-dirs(fs1, ri1)[m0, mkdir(m6 + 1, md2, m1, m2, abs-children(m0, fs1, ri1)[str, n])], (abs-files(fs1, ri1) ++ n)[n, mkfile(0, md, 1, ∅)]), file-node-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), file-node-cons(fs1, ri1), log-cons (log0, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ]), log-cons(log0, fs1), orphans-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1)), orphans-cons(fs1, ri1, orphans(fs1, ri1)), replay-cons-strong (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ri-inj(ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), ri-inj(ri1), ri-inj(fi), ubifs-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), inodekey(m0) ∈ ri1, ri1[inodekey(m0)] ∈ fs1, asynced0 → boolvar0, links(m0, abs-dirs(fs1, ri1)) ≠ ∅ ∨ m0 = ROOT_INO, m1 ≠ 0 ∨ m0 = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, inodekey(ino) = inodekey(n), m0 = 0, n = 0, adr3 ∈ fs1, adr2 ∈ fs1, adr1 ∈ fs1, inodekey(n) ∈ ri1, inodekey(n) ∈ fo, dentrykey(m0, str) ∈ ri1, ( 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, false, 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, m6 + 1) ;fs1[(n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)]))] ) ) ) .directory) ∧ ( ino = n ∨ inodekey(ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(ino)]].directory → (ino = n ⊃ mkfile(0, md, 1, ∅);(abs-files(fs1, ri1) ++ n)[ino]) = mkfile ((adr3 = (n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)])) ⊃ inodenode(inodekey(n), md, false, 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, 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, false, 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, 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, false, 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, m6 + 1) ;fs1[(n = ino ⊃ adr3;(m0 = ino ⊃ adr1;ri1[inodekey(ino)]))] ) ) ) .nlink, abs-content (ino, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, false, 1, 0, 0) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]))), m1 = 0 ∧ m0 ≠ ROOT_INO

Rule argument

fma: inodekey(ino) = inodekey(n)

Additional information

Used simplifier rules: ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).meta = md; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ key ∈ ri[key, adr]; (s)%⊦ mkfile(m0, md0, n0, content0) = mkfile(m1, md1, n1, content1) ↔ ¬(n0 ≠ n1 ∨ md0 ≠ md1 ∨ m0 ≠ m1 ∨ content0 ≠ content1); (ss)%⊦ content = abs-content(ino, fs, ri) ↔ (∀ n. (n ∈ content ↔ datakey(ino, n) ∈ ri) ∧ (n ∈ content → content[n] = fs[ri[datakey(ino, n)]].data)); (ss)% ⊦ ¬ n ∈ ∅; (s)% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (las)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ datakey(m, m0) ≠ dentrykey(m1, str); (s)%ubifs-file-notdir: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ fs[ri[inodekey(ino)]].directory; (forward) from specification aubifs-inv%ubifs-file-in: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv% ⊦ ¬ key ∈ ri → ri[key] = (∅)[key]; (s)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (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)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)%⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri); (s)%⊦ abs-file(ino, fs, ri) = mkfile (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)); (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set] Used formulas: inodekey(ino) = inodekey(n)