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Proof step 416 from proof refine-rename-overwrite-reparent-file (previous step)

m12 + 1 = fs0[ri0[inodekey(m0)]].nlink, 0 = fs0[ri0[inodekey(m0)]].nsubdirs, abs-dirs(fs0, ri0)[m4] = mkdir(m16, md6, m17, m18, entries0), fs0[ri0[inodekey(m)]] = inodenode(key, md5, false, m10, 0, m13), fs0[ri0[inodekey(m9)]] = inodenode(key1, md3, true, m1, m3, m14 + 1), fs0[ri0[dentrykey(m9, str)]] = dentrynode(key3, m), fs0[ri0[dentrykey(m4, str0)]] = dentrynode(key0, m0), fs0[ri0[inodekey(m4)]] = inodenode(key2, md4, true, m6, m7, m8), 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(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)][adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14)] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, m12, 0, m5) ], (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4][inodekey(m0), adr5]), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)][adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14)] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, m12, 0, m5) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, dentrynode(dentrykey(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)][adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14)] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, m12, 0, m5) ], (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4][inodekey(m0), adr5], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)][adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14)] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, m12, 0, m5) ], (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4][inodekey(m0), adr5], orphans(fs0, ri0), 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(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4][inodekey(m0), adr5]), ri-inj(fi), ri-inj(ri0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)][adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14)] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, m12, 0, m5) ], (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4][inodekey(m0), adr5], orphans(fs0, ri0), fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), dentrykey(m9, str) ∈ ri0, inodekey(m0) ∈ ri0, dentrykey(m4, str0) ∈ ri0, inodekey(m4) ∈ ri0, ri0[dentrykey(m4, str0)] ∈ fs0, ri0[inodekey(m4)] ∈ fs0, ri0[inodekey(m9)] ∈ fs0, ri0[dentrykey(m9, str)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(m9) ∈ ri0, boolvar2 → boolvar0, links(m9, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m9 = ROOT_INO, links(m4, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m4 = ROOT_INO, m1 ≠ 0 ∨ m9 = ROOT_INO, m6 ≠ 0 ∨ m4 = 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, m12 = 0, m4 = 0, m9 = m4, m9 = 0, fs0[ri0[inodekey(m0)]].directory, adr4 ∈ (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3], adr2 ∈ ri0 -- dentrykey(m9, str), adr5 ∈ fs0, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2], adr5 ∈ (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4], m6 = 0 ∧ m4 ≠ ROOT_INO, m1 = 0 ∧ m9 ≠ ROOT_INO, str0 ∈ entries0 ∧ m0 = entries0[str0] ∧ m6 = m17 ∧ m8 = m16 ∧ m7 = m18

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-abs name: at-dirs seq: ⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri) subst: [ino, ri, fs] → [m4, ri0, fs0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 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)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)% ⊦ dentrynode(key, m).ino = m; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss) Used terms: m4, ri0, fs0