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Proof step 138 from proof refine-rename-new-keep-parent (previous step)

fs0[ri0[dentrykey(m3, str)]] = dentrynode(key1, m), fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, true, m4, m1 + 1, m0 + 1), fs0[ri0[inodekey(m)]].directory, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0)[m3, mkdir(m0 + 1, md0, m4, m1 + 1, (abs-children(m3, fs0, ri0) -- str)[str0, m])], abs-files(fs0, ri0)), file-node-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1)]), log-cons(log0, fs0), orphans-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-inj((ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(m) ∈ ri0, dentrykey(m3, str) ∈ ri0, inodekey(m3) ∈ ri0, ri0[inodekey(m3)] ∈ fs0, ri0[dentrykey(m3, str)] ∈ fs0, boolvar3 → boolvar4, m4 ≠ 0 ∨ m3 = ROOT_INO, links(m3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m3 = ROOT_INO ⊦ abs-dirs(fs0, ri0)[m3, mkdir(m0 + 1, md0, m4, m1 + 1, (abs-children(m3, fs0, ri0) -- str)[str0, m])] = abs-dirs (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), adr1 = adr3, adr1 = adr2, adr2 = adr3, m3 = 0, adr3 ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2], dentrykey(m3, str0) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m3, str), m4 = 0 ∧ m3 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 139:
fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, true, m4, m1 + 1, m0 + 1), fs0[ri0[dentrykey(m3, str)]] = dentrynode(key1, m), fs0[ri0[inodekey(m)]].directory, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0)[m3, mkdir(m0 + 1, md0, m4, m1 + 1, (abs-children(m3, fs0, ri0) -- str)[str0, m])], abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1)]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri0), ri-inj((ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri0[dentrykey(m3, str)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, inodekey(m3) ∈ ri0, dentrykey(m3, str) ∈ ri0, inodekey(m) ∈ ri0, boolvar3 → boolvar4, links(m3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m3 = ROOT_INO, m4 ≠ 0 ∨ m3 = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, m3 = 0, adr2 ∈ ri0 -- dentrykey(m3, str), adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, dentrykey(m3, str0) ∈ ri0, adr3 ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2], m4 = 0 ∧ m3 ≠ ROOT_INO, ( inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].directory ↔ inodekey(ino) ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3] ∧ (adr3 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1) ;(adr2 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m3, str0), m) ;(adr1 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m3, str), 0);fs0[(m3 = ino ⊃ adr3;ri0[inodekey(ino)])]) ) ) .directory) ∧ ( inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].directory → (ino = m3 ⊃ mkdir(m0 + 1, md0, m4, m1 + 1, (abs-children(m3, fs0, ri0) -- str)[str0, 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 ((adr3 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1) ;(adr2 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m3, str0), m) ;(adr1 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m3, str), 0);fs0[(m3 = ino ⊃ adr3;ri0[inodekey(ino)])]) ) ) .size, (adr3 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1) ;(adr2 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m3, str0), m) ;(adr1 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m3, str), 0);fs0[(m3 = ino ⊃ adr3;ri0[inodekey(ino)])]) ) ) .meta, (adr3 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1) ;(adr2 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m3, str0), m) ;(adr1 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m3, str), 0);fs0[(m3 = ino ⊃ adr3;ri0[inodekey(ino)])]) ) ) .nlink, (adr3 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1) ;(adr2 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m3, str0), m) ;(adr1 = (m3 = ino ⊃ adr3;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m3, str), 0);fs0[(m3 = ino ⊃ adr3;ri0[inodekey(ino)])]) ) ) .nsubdirs, abs-children (ino, fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, m4, m1 + 1, m0 + 1) ], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3])))

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)%key ≠ key0 ⊦ (ri -- key0)[key] = ri[key]; (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)