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Proof step 202 from proof refine-rmdir (previous step)

(m = m4 ⊃ mkdir(m5, md0, m2, m7, entries);mkdir(m1, md, m3, m0, abs-children(m, fs0, ri0) -- str)) = mkdir(m6, md4, m8, m9, entries0), (m4 = m ⊃ mkdir(m1, md1, m3, m0, abs-children(m, fs0, ri0) -- str) ;mkdir(fs0[ri0[inodekey(m4)]].size, fs0[ri0[inodekey(m4)]].meta, 1, fs0[ri0[inodekey(m4)]].nsubdirs, ∅) ) = mkdir(m5, md3, m2 + 1, m7, entries), (m4 = m ⊃ mkdir(m5, md, m2, m7, entries);mkdir(m5, md3, m2, m7, entries)) = mkdir(m10, md5, m11, m12, entries1), 1 = fs0[ri0[inodekey(m4)]].nlink, fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m3, m0 + 1, m1 + 1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m4), fs0[ri0[inodekey(m4)]] = inodenode(key1, md2, true, 1, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size), abs-children(m4, fs0, ri0) = ∅, dentrykeys(inodekey(m4), ri0) = ∅, links(m4, fs0, ri0) = ∅ ++ dentrykey(m, str), fs0[ri0[inodekey(m4)]].directory, fs0[ri0[inodekey(m4)]].inode?, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons (abs-dirs(fs0, ri0)[m, (m = m4 ⊃ mkdir(m5, md3, m2, m7, entries);mkdir(m1, md1, m3, m0, abs-children(m, fs0, ri0) -- str)).meta:= md] [m4, mkdir(m10, md0, m11, m12, entries1) ], abs-files(fs0, ri0)), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4), 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(m4), adr3]), ri-inj(fi), ri-inj(ri0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4), 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(m4) ∈ ri0, ri0[inodekey(m4)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, asynced0 → boolvar0, m3 ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, m4 = ROOT_INO, m4 = 0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, m3 = 0 ∧ m ≠ ROOT_INO, abs-dirs(fs0, ri0)[m, (m = m4 ⊃ mkdir(m5, md3, m2, m7, entries);mkdir(m1, md1, m3, m0, abs-children(m, fs0, ri0) -- str)).meta:= md] [m4, mkdir(m10, md0, m11, m12, entries1) ] = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]) ∧ abs-files(fs0, ri0) = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]) ∧ orphans (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]) = orphans(fs0, ri0) ++ inodekey(m4) ∧ mkinode(m, md, true, m3, m0, m1) = mkinode(m, md4, true, m8, m9, m6) ∧ mkinode(m4, md0, true, 0, fs0[ri0[inodekey(m4)]].nsubdirs, fs0[ri0[inodekey(m4)]].size) = mkinode(m4, md0, true, m11, m12, m10)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 203:
(m4 = m ⊃ mkdir(m5, md, m2, m7, entries);mkdir(m5, md3, m2, m7, entries)) = mkdir(m10, md5, m11, m12, entries1), (m4 = m ⊃ mkdir(m1, md1, m3, m0, abs-children(m, fs0, ri0) -- str);mkdir(m15, md6, 1, m14, ∅)) = mkdir(m5, md3, m2 + 1, m7, entries), (m = m4 ⊃ mkdir(m5, md0, m2, m7, entries);mkdir(m1, md, m3, m0, abs-children(m, fs0, ri0) -- str)) = mkdir(m6, md4, m8, m9, entries0), 1 = m13, fs0[ri0[inodekey(m4)]] = inodenode(key1, md2, true, 1, m14, m15), fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m4), fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m3, m0 + 1, m1 + 1), fs0[ri0[inodekey(m4)]] = inodenode(key2, md6, boolvar, m13, m14, m15), abs-children(m4, fs0, ri0) = ∅, boolvar, dentrykeys(inodekey(m4), ri0) = ∅, links(m4, fs0, ri0) = ∅ ++ dentrykey(m, str), fs0[ri0[inodekey(m4)]].inode?, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons (abs-dirs(fs0, ri0)[m, (m = m4 ⊃ mkdir(m5, md3, m2, m7, entries);mkdir(m1, md1, m3, m0, abs-children(m, fs0, ri0) -- str)).meta:= md] [m4, mkdir(m10, md0, m11, m12, entries1) ], abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m14, m15) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m14, m15) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m14, m15) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m14, m15) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m14, m15) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3], orphans(fs0, ri0) ++ inodekey(m4), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m4)] ∈ fs0, inodekey(m4) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, dentrykey(m, str) ∈ ri0, asynced0 → boolvar0, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, m3 ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, m4 = 0, m4 = ROOT_INO, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, abs-dirs(fs0, ri0)[m, (m = m4 ⊃ mkdir(m5, md3, m2, m7, entries);mkdir(m1, md1, m3, m0, abs-children(m, fs0, ri0) -- str)).meta:= md] [m4, mkdir(m10, md0, m11, m12, entries1) ] = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m14, m15) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]) ∧ abs-files(fs0, ri0) = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m14, m15) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]) ∧ orphans (fs0[adr1, inodenode(inodekey(m), md, true, m3, m0, m1)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m4), md0, true, 0, m14, m15) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m4), adr3]) = orphans(fs0, ri0) ++ inodekey(m4) ∧ mkinode(m, md, true, m3, m0, m1) = mkinode(m, md4, true, m8, m9, m6) ∧ mkinode(m4, md0, true, 0, m14, m15) = mkinode(m4, md0, true, m11, m12, m10), m3 = 0 ∧ m ≠ ROOT_INO

Rule argument

spec: node name: elim-03 seq: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)) subst: [nd, key, md, boolvar, m, m0, m1] → [fs0[ri0[inodekey(m4)]], key2, md6, boolvar, m13, m14, m15]

Additional information

Used simplifier rules: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)); (elim) Used terms: fs0[ri0[inodekey(m4)]], key2, md6, boolvar, m13, m14, m15