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Proof step 666 from proof refine-rename-overwrite-reparent-dir (previous step)

1 = fs0[ri0[inodekey(m0)]].nlink, abs-dirs(fs0, ri0)[m7] = mkdir(m5, md, m6, m8, entries), fs0[ri0[inodekey(m)]] = inodenode(key, md6, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size), fs0[ri0[inodekey(m7)]] = inodenode(key1, md3, true, m1, m2, m3), fs0[ri0[dentrykey(m11, str)]] = dentrynode(key4, m), fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m0), fs0[ri0[inodekey(m11)]] = inodenode(key2, md4, true, m4, m16 + 1, m13 + 1), fs0[ri0[inodekey(m0)]] = inodenode(key3, md5, true, 1, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size), abs-children(m0, fs0, ri0) = ∅, dentrykeys(inodekey(m0), ri0) = ∅, dirs = abs-dirs(fs0, ri0)[m11, mkdir(m13, md4, m4, m16, abs-children(m11, fs0, ri0) -- str)][m7, mkdir(m5, md, m6, m8, entries[str0, m])], files = abs-files(fs0, ri0), ino = mkdentry(str0, m0).ino, links(m0, fs0, ri0) = ∅ ++ dentrykey(m7, str0), mkdentry(str0, m0).dentry?, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m0)]].directory, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ]), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0)), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0), fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj((ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0), fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(m7, str0) ∈ ri0, inodekey(m0) ∈ ri0, dentrykey(m11, str) ∈ ri0, inodekey(m7) ∈ ri0, inodekey(m11) ∈ ri0, ri0[dentrykey(m7, str0)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[inodekey(m11)] ∈ fs0, ri0[dentrykey(m11, str)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, boolvar2 → boolvar3, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m11 = ROOT_INO, m1 ≠ 0 ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m11 = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr1 = adr5, adr2 = adr3, adr2 = adr4, adr2 = adr5, adr3 = adr4, adr3 = adr5, adr4 = adr5, m0 = ROOT_INO, m0 = 0, m11 = m7, m11 = 0, m7 = 0, adr4 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3], adr2 ∈ ri0 -- dentrykey(m11, str), adr5 ∈ fs0, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2], adr5 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4], dirs[ino].nlink ≥ 1, m4 = 0 ∧ m11 ≠ ROOT_INO, m1 = 0 ∧ m7 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 667:
(m0 = m7 ⊃ mkdir(m5, md, m6, m8, entries[str0, m]) ;(m0 = m11 ⊃ mkdir(m13, md4, m4, m16, abs-children(m11, fs0, ri0) -- str) ;mkdir(fs0[ri0[inodekey(m0)]].size, fs0[ri0[inodekey(m0)]].meta, 1, fs0[ri0[inodekey(m0)]].nsubdirs, ∅) ) ) .nlink = 0, 1 = fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]] = inodenode(key3, md5, true, 1, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size), fs0[ri0[inodekey(m11)]] = inodenode(key2, md4, true, m4, m16 + 1, m13 + 1), fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m0), fs0[ri0[dentrykey(m11, str)]] = dentrynode(key4, m), fs0[ri0[inodekey(m7)]] = inodenode(key1, md3, true, m1, m2, m3), fs0[ri0[inodekey(m)]] = inodenode(key, md6, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size), abs-dirs(fs0, ri0)[m7] = mkdir(m5, md, m6, m8, entries), abs-children(m0, fs0, ri0) = ∅, dentrykeys(inodekey(m0), ri0) = ∅, links(m0, fs0, ri0) = ∅ ++ dentrykey(m7, str0), fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(m)]].directory, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ]), orphans-cons (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0), fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ri-inj((ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0), fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, ri0[dentrykey(m11, str)] ∈ fs0, ri0[inodekey(m11)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, ri0[dentrykey(m7, str0)] ∈ fs0, inodekey(m11) ∈ ri0, inodekey(m7) ∈ ri0, dentrykey(m11, str) ∈ ri0, inodekey(m0) ∈ ri0, dentrykey(m7, str0) ∈ ri0, boolvar2 → boolvar3, m4 ≠ 0 ∨ m11 = ROOT_INO, m1 ≠ 0 ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m11 = ROOT_INO, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO ⊦ adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, m0 = 0, m0 = ROOT_INO, m11 = 0, m11 = m7, m7 = 0, adr5 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4], adr3 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2], adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m11, str), adr4 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3], m1 = 0 ∧ m7 ≠ ROOT_INO, m4 = 0 ∧ m11 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ m < 1 ↔ m = 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n ≥ m ↔ m ≤ n; (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)%⊦ 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)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ mkdentry(str, m).dentry?; (s)