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Proof step 181 from proof refine-create (previous step)

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, inodekey(ino) ∈ ri1, asynced0 → boolvar0, links(m0, abs-dirs(fs1, ri1)) ≠ ∅ ∨ m0 = ROOT_INO, m1 ≠ 0 ∨ m0 = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr1 = ri1[inodekey(ino)], adr2 = adr3, adr2 = ri1[inodekey(ino)], adr3 = ri1[inodekey(ino)], m0 = 0, m0 = ino, n = 0, fs1[ri1[inodekey(ino)]].directory, adr3 ∈ fs1, adr2 ∈ fs1, adr1 ∈ fs1, inodekey(n) ∈ ri1, inodekey(n) ∈ fo, dentrykey(m0, str) ∈ ri1, (¬ fs1[ri1[inodekey(ino)]].directory → inodekey(ino) ∈ ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]) ∧ ( ¬ fs1[ri1[inodekey(ino)]].directory → mkfile(fs1[ri1[inodekey(ino)]].size, fs1[ri1[inodekey(ino)]].meta, fs1[ri1[inodekey(ino)]].nlink, abs-content(ino, fs1, ri1)) = mkfile (fs1[ri1[inodekey(ino)]].size, fs1[ri1[inodekey(ino)]].meta, fs1[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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 182:
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, inodekey(ino) ∈ ri1, asynced0 → boolvar0, links(m0, abs-dirs(fs1, ri1)) ≠ ∅ ∨ m0 = ROOT_INO, m1 ≠ 0 ∨ m0 = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr1 = ri1[inodekey(ino)], adr2 = adr3, adr2 = ri1[inodekey(ino)], adr3 = ri1[inodekey(ino)], m0 = 0, m0 = ino, n = 0, fs1[ri1[inodekey(ino)]].directory, adr3 ∈ fs1, adr2 ∈ fs1, adr1 ∈ fs1, inodekey(n) ∈ ri1, inodekey(n) ∈ fo, dentrykey(m0, str) ∈ ri1, m1 = 0 ∧ m0 ≠ ROOT_INO, (datakey(ino, n0) ∈ ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3] ↔ datakey(ino, n0) ∈ ri1) ∧ ( datakey(ino, n0) ∈ ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3] → (adr3 = ri1[datakey(ino, n0)] ⊃ inodenode(inodekey(n), md, false, 1, 0, 0) ;(adr2 = ri1[datakey(ino, n0)] ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = ri1[datakey(ino, n0)] ⊃ inodenode(inodekey(m0), md2, true, m1, m2, m6 + 1);fs1[ri1[datakey(ino, n0)]]) ) ) .data = fs1[ri1[datakey(ino, n0)]].data)

Rule argument

Additional information

Used simplifier rules: at-ri: ⊦ ri[key, adr][key0] = (key = key0 ⊃ adr;ri[key0]);% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (las)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ datakey(m, m0) ≠ dentrykey(m1, str); (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)%⊦ datakey(ino, n) ∈ ri → abs-content(ino, fs, ri)[n] = fs[ri[datakey(ino, n)]].data; (s)% ⊦ n ∈ abs-content(ino, fs, ri) ↔ datakey(ino, n) ∈ ri; (s)%⊦ content = abs-content(ino, fs, ri) ↔ (∀ n. (n ∈ content ↔ datakey(ino, n) ∈ ri) ∧ (n ∈ content → content[n] = fs[ri[datakey(ino, n)]].data)); (ss)%⊦ mkfile(m0, md0, n0, content0) = mkfile(m1, md1, n1, content1) ↔ ¬(n0 ≠ n1 ∨ md0 ≠ md1 ∨ m0 ≠ m1 ∨ content0 ≠ content1); (ss)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (ws)