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Proof step 411 from proof refine-unlink (previous step)

m5 + 1 = fs0[ri0[inodekey(m1)]].nlink, 0 = fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m2, m3, m0 + 1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m1), inodekey(ino) = inodekey(m1), orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons (abs-dirs(fs0, ri0)[m, mkdir(m0, md, m2, m3, abs-children(m, fs0, ri0) -- str)], abs-files(fs0, ri0)[m1, mkfile(m6, md0, m5, abs-content(m1, fs0, ri0))]), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(ino) ∈ ri0, dentrykey(m, str) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, asynced0 → boolvar0, m2 ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, m = ino, m1 = ROOT_INO, m1 = 0, m5 = 0, fs0[ri0[inodekey(m1)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, ( ¬ fs0[ri0[inodekey(ino)]].directory ↔ inodekey(ino) ∈ (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3] ∧ ¬ (adr3 = (m1 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m1), md0, false, m5, 0, m6) ;(adr2 = (m1 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = (m1 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, true, m2, m3, m0);fs0[(m1 = ino ⊃ adr3;ri0[inodekey(ino)])]) ) ) .directory) ∧ ( ¬ fs0[ri0[inodekey(ino)]].directory → (ino = m1 ⊃ mkfile(m6, md0, m5, abs-content(m1, fs0, ri0)) ;mkfile(fs0[ri0[inodekey(ino)]].size, fs0[ri0[inodekey(ino)]].meta, fs0[ri0[inodekey(ino)]].nlink, abs-content(ino, fs0, ri0)) ) = mkfile ((adr3 = (m1 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m1), md0, false, m5, 0, m6) ;(adr2 = (m1 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = (m1 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, true, m2, m3, m0);fs0[(m1 = ino ⊃ adr3;ri0[inodekey(ino)])]) ) ) .size, (adr3 = (m1 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m1), md0, false, m5, 0, m6) ;(adr2 = (m1 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = (m1 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, true, m2, m3, m0);fs0[(m1 = ino ⊃ adr3;ri0[inodekey(ino)])]) ) ) .meta, (adr3 = (m1 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m1), md0, false, m5, 0, m6) ;(adr2 = (m1 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = (m1 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, true, m2, m3, m0);fs0[(m1 = ino ⊃ adr3;ri0[inodekey(ino)])]) ) ) .nlink, abs-content (ino, fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3])))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 412:
m5 + 1 = fs0[ri0[inodekey(m1)]].nlink, 0 = fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m2, m3, m0 + 1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m1), orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons (abs-dirs(fs0, ri0)[m, mkdir(m0, md, m2, m3, abs-children(m, fs0, ri0) -- str)], abs-files(fs0, ri0)[m1, mkfile(m6, md0, m5, abs-content(m1, fs0, ri0))]), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3]), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m2, m3, m0)][adr2, dentrynode(dentrykey(m, str), 0)][adr3, inodenode(inodekey(m1), md0, false, m5, 0, m6)], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(m, str) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, asynced0 → boolvar0, m2 ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, m = m1, m1 = ROOT_INO, m1 = 0, m5 = 0, fs0[ri0[inodekey(m1)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, (datakey(m1, n) ∈ (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3] ↔ datakey(m1, n) ∈ ri0) ∧ ( datakey(m1, n) ∈ (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m1), adr3] → (adr3 = ri0[datakey(m1, n)] ⊃ inodenode(inodekey(m1), md0, false, m5, 0, m6) ;(adr2 = ri0[datakey(m1, n)] ⊃ dentrynode(dentrykey(m, str), 0) ;(adr1 = ri0[datakey(m1, n)] ⊃ inodenode(inodekey(m), md, true, m2, m3, m0);fs0[ri0[datakey(m1, n)]]) ) ) .data = fs0[ri0[datakey(m1, n)]].data)

Rule argument

Additional information

Used simplifier rules: at-ri: ⊦ ri[key, adr][key0] = (key = key0 ⊃ adr;ri[key0]);% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)%key ≠ key0 ⊦ (ri -- key0)[key] = ri[key]; (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)% ⊦ key ∈ ri[key, adr]; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).meta = md; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)