[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 436 from proof refine-rename-overwrite-keep-parent-identity (previous step)

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), 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, boolvar3, m0, m1, 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, boolvar3, m0, m1, 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, boolvar3, m0, m1, 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, boolvar3, m0, m1, 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, boolvar3, m0, m1, 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, boolvar2 → 1 ≤ m8, m0 = 1 → links(m, fs0, ri0) = ∅ ++ dentrykey(m6, str), boolvar4 → boolvar1, fs0[ri0[inodekey(m)]].directory → abs-children(m, fs0, ri0) = ∅, fs0[ri0[inodekey(m)]].directory → dentrykeys(inodekey(m), ri0) = ∅, m7 ≠ 0 ∨ m6 = ROOT_INO, links(m6, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m6 = ROOT_INO, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m4 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar2 ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m4 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m5 = fs0[ri0[inodekey(m)]].size, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar3 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar3 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].directory ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m5 = fs0[ri0[inodekey(m)]].size ∧ m4 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar2 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m4 = 0 ∧ ¬ boolvar2, fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m2 = fs0[ri0[inodekey(m)]].size ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar3 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar3 ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m = ROOT_INO, m = 0, m0 = 0, m6 = 0, m9 = 0, adr2 ∈ ri0 -- dentrykey(m6, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, m7 = 0 ∧ m6 ≠ ROOT_INO, str ∈ abs-dirs(fs0, ri0)[m6].entries ∧ m = abs-dirs(fs0, ri0)[m6].entries[str] ∧ m7 = abs-dirs(fs0, ri0)[m6].nlink ∧ m9 = abs-dirs(fs0, ri0)[m6].size ∧ m8 = abs-dirs(fs0, ri0)[m6].nsubdirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 437:
fs0[ri0[dentrykey(m6, str)]] = dentrynode(key1, m), fs0[ri0[inodekey(m6)]] = inodenode(key0, md2, true, m7, m8, m9), abs-dirs(fs0, ri0)[m6] = mkdir(m10, md0, m11, m12, entries), 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(m6, str), 0)][adr2, dentrynode(dentrykey(m6, str), m)][adr3, inodenode(inodekey(m6), md1, true, m7, m8, m9)] [adr4, inodenode(inodekey(m), md, boolvar3, m0, m1, 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, boolvar3, m0, m1, 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, boolvar3, m0, m1, 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, boolvar3, m0, m1, 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, boolvar3, m0, m1, 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, fs0[ri0[inodekey(m)]].directory → dentrykeys(inodekey(m), ri0) = ∅, fs0[ri0[inodekey(m)]].directory → abs-children(m, fs0, ri0) = ∅, boolvar4 → boolvar1, m0 = 1 → links(m, fs0, ri0) = ∅ ++ dentrykey(m6, str), boolvar2 → 1 ≤ m8, fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m2 = fs0[ri0[inodekey(m)]].size ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar3 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar3, fs0[ri0[inodekey(m)]].directory ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m5 = fs0[ri0[inodekey(m)]].size ∧ m4 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar2 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m4 = 0 ∧ ¬ boolvar2, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar3 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar3 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri0[inodekey(m)]].size, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m4 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar2 ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m4 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m5 = fs0[ri0[inodekey(m)]].size, links(m6, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m6 = ROOT_INO, m7 ≠ 0 ∨ m6 = ROOT_INO ⊦ adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m = ROOT_INO, m0 = 0, m6 = 0, m9 = 0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m6, str), str ∈ entries ∧ m = entries[str] ∧ m7 = m11 ∧ m9 = m10 ∧ m8 = m12, m7 = 0 ∧ m6 ≠ ROOT_INO

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [abs-dirs(fs0, ri0)[m6], m10, md0, m11, m12, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: abs-dirs(fs0, ri0)[m6], m10, md0, m11, m12, entries