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Proof step 163 from proof refine-rename-overwrite-keep-parent-identity (previous step)

fs0[ri0[inodekey(m)]].nsubdirs = 0, fs0[ri0[inodekey(m6)]] = inodenode(key0, md2, true, m7, m8, m9), fs0[ri0[dentrykey(m6, str)]] = dentrynode(key1, m), orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons (abs-dirs(fs0, ri0)[m6, mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m])], abs-files(fs0, ri0)[m, mkfile(m2, md, fs0[ri0[inodekey(m)]].nlink, abs-content(m, fs0, ri0))]), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, dentrynode(dentrykey(m6, str), 0)][adr2, dentrynode(dentrykey(m6, str), m)][adr3, inodenode(inodekey(m6), md1, true, m7, m8, m9)] [adr4, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m6, str), 0)][adr2, dentrynode(dentrykey(m6, str), m)][adr3, inodenode(inodekey(m6), md1, true, m7, m8, m9)] [adr4, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, dentrynode(dentrykey(m6, str), 0)][adr2, dentrynode(dentrykey(m6, str), m)][adr3, inodenode(inodekey(m6), md1, true, m7, m8, m9)] [adr4, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m6, str), 0)][adr2, dentrynode(dentrykey(m6, str), m)][adr3, inodenode(inodekey(m6), md1, true, m7, m8, m9)] [adr4, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4], orphans(fs0, ri0), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m6, str), 0)][adr2, dentrynode(dentrykey(m6, str), m)][adr3, inodenode(inodekey(m6), md1, true, m7, m8, m9)] [adr4, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4], orphans(fs0, ri0), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri0[inodekey(m6)] ∈ fs0, ri0[dentrykey(m6, str)] ∈ fs0, inodekey(m6) ∈ ri0, inodekey(m) ∈ ri0, dentrykey(m6, str) ∈ ri0, 1 ≤ m9, fs0[ri0[inodekey(m)]].nlink = 1 → links(m, fs0, ri0) = ∅ ++ dentrykey(m6, str), boolvar4 → boolvar1, m7 ≠ 0 ∨ m6 = ROOT_INO, links(m6, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m6 = ROOT_INO ⊦ fs0[ri0[inodekey(m)]].nlink = 0, abs-dirs(fs0, ri0)[m6, mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m])] = abs-dirs (fs0[adr1, dentrynode(dentrykey(m6, str), 0)][adr2, dentrynode(dentrykey(m6, str), m)][adr3, inodenode(inodekey(m6), md1, true, m7, m8, m9)] [adr4, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]), adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m = ROOT_INO, m = 0, m6 = 0, m9 = 0, fs0[ri0[inodekey(m)]].directory, adr2 ∈ ri0 -- dentrykey(m6, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, m7 = 0 ∧ m6 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 164:
fs0[ri0[inodekey(m)]].nsubdirs = 0, fs0[ri0[dentrykey(m6, str)]] = dentrynode(key1, m), fs0[ri0[inodekey(m6)]] = inodenode(key0, md2, true, m7, m8, m9), fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons (abs-dirs(fs0, ri0)[m6, mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m])], abs-files(fs0, ri0)[m, mkfile(m2, md, fs0[ri0[inodekey(m)]].nlink, abs-content(m, fs0, ri0))]), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, dentrynode(dentrykey(m6, str), 0)][adr2, dentrynode(dentrykey(m6, str), m)][adr3, inodenode(inodekey(m6), md1, true, m7, m8, m9)] [adr4, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m6, str), 0)][adr2, dentrynode(dentrykey(m6, str), m)][adr3, inodenode(inodekey(m6), md1, true, m7, m8, m9)] [adr4, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, dentrynode(dentrykey(m6, str), 0)][adr2, dentrynode(dentrykey(m6, str), m)][adr3, inodenode(inodekey(m6), md1, true, m7, m8, m9)] [adr4, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4], orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m6, str), 0)][adr2, dentrynode(dentrykey(m6, str), m)][adr3, inodenode(inodekey(m6), md1, true, m7, m8, m9)] [adr4, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4], orphans(fs0, ri0), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ri-inj(ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m6, str), 0)][adr2, dentrynode(dentrykey(m6, str), m)][adr3, inodenode(inodekey(m6), md1, true, m7, m8, m9)] [adr4, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4], orphans(fs0, ri0), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), dentrykey(m6, str) ∈ ri0, inodekey(m) ∈ ri0, inodekey(m6) ∈ ri0, ri0[dentrykey(m6, str)] ∈ fs0, ri0[inodekey(m6)] ∈ fs0, 1 ≤ m9, boolvar4 → boolvar1, fs0[ri0[inodekey(m)]].nlink = 1 → links(m, fs0, ri0) = ∅ ++ dentrykey(m6, str), links(m6, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m6 = ROOT_INO, m7 ≠ 0 ∨ m6 = ROOT_INO ⊦ fs0[ri0[inodekey(m)]].nlink = 0, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m = ROOT_INO, m6 = 0, m9 = 0, fs0[ri0[inodekey(m)]].directory, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m6, str), m7 = 0 ∧ m6 ≠ ROOT_INO, ( inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].directory ↔ inodekey(ino) ∈ ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4] ∧ (adr4 = (m = ino ⊃ adr4;(m6 = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ;(adr3 = (m = ino ⊃ adr4;(m6 = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m6), md1, true, m7, m8, m9) ;(adr2 = (m = ino ⊃ adr4;(m6 = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m6, str), m) ;(adr1 = (m = ino ⊃ adr4;(m6 = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m6, str), 0) ;fs0[(m = ino ⊃ adr4;(m6 = ino ⊃ adr3;ri0[inodekey(ino)]))] ) ) ) ) .directory) ∧ ( inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].directory → (ino = m6 ⊃ mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m]) ;mkdir (fs0[ri0[inodekey(ino)]].size, fs0[ri0[inodekey(ino)]].meta, fs0[ri0[inodekey(ino)]].nlink, fs0[ri0[inodekey(ino)]].nsubdirs, abs-children(ino, fs0, ri0)) ) = mkdir ((adr4 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ;(adr3 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m6), md1, true, m7, m8, m9) ;(adr2 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m6, str), m) ;(adr1 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m6, str), 0);fs0[(m6 = ino ⊃ adr3;ri0[inodekey(ino)])]) ) ) ) .size, (adr4 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ;(adr3 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m6), md1, true, m7, m8, m9) ;(adr2 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m6, str), m) ;(adr1 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m6, str), 0);fs0[(m6 = ino ⊃ adr3;ri0[inodekey(ino)])]) ) ) ) .meta, (adr4 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ;(adr3 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m6), md1, true, m7, m8, m9) ;(adr2 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m6, str), m) ;(adr1 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m6, str), 0);fs0[(m6 = ino ⊃ adr3;ri0[inodekey(ino)])]) ) ) ) .nlink, (adr4 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ;(adr3 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m6), md1, true, m7, m8, m9) ;(adr2 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m6, str), m) ;(adr1 = (m6 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m6, str), 0);fs0[(m6 = ino ⊃ adr3;ri0[inodekey(ino)])]) ) ) ) .nsubdirs, abs-children (ino, fs0[adr1, dentrynode(dentrykey(m6, str), 0)][adr2, dentrynode(dentrykey(m6, str), m)][adr3, inodenode(inodekey(m6), md1, true, m7, m8, m9)] [adr4, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4])))

Rule argument

Additional information

Used simplifier rules: at-ri: ⊦ ri[key, adr][key0] = (key = key0 ⊃ adr;ri[key0]);%⊦ 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)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)% ⊦ 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 ∈ 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)