[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 289 from proof refine-rename-overwrite-keep-parent-identity (previous step)

(m6 = m ⊃ mkdir(m9, md, m7, m8, (∅)[str, m]);mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m])) = mkdir(m0, md0, m1, m2, entries), fs0[ri0[dentrykey(m6, str)]] = dentrynode(key1, m), fs0[ri0[inodekey(m6)]] = inodenode(key0, md2, true, m7, m8, m9), abs-children(m, fs0, ri0) = ∅, dentrykeys(inodekey(m), ri0) = ∅, fs0[ri0[inodekey(m)]].directory, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons (abs-dirs(fs0, ri0)[m6, mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m])] [m, (m = m6 ⊃ mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m6]) ;mkdir(fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].meta, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, ∅) ) .meta:= md ], 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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ], 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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ]), 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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ], 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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ], 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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ], 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, 1 ≤ m8, boolvar4 → boolvar1, fs0[ri0[inodekey(m)]].nlink = 1 → links(m, fs0, ri0) = ∅ ++ dentrykey(m6, str), links(m6, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m6 = ROOT_INO, m7 ≠ 0 ∨ m6 = ROOT_INO ⊦ fs0[ri0[inodekey(m)]].nlink = 0, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m = ROOT_INO, m6 = 0, m8 = 0, m9 = 0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m6, str), m7 = 0 ∧ m6 ≠ ROOT_INO, abs-dirs(fs0, ri0)[m6, mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m])] [m, (m = m6 ⊃ mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m6]) ;mkdir(fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].meta, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, ∅) ) .meta:= md ] = abs-dirs (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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]) ∧ abs-files(fs0, ri0) = abs-files (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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]) ∧ orphans (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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]) = orphans(fs0, ri0) ∧ mkinode(m6, md1, true, m7, m8, m9) = mkinode(m6, md0, true, m1, m2, m0) ∧ mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) = mkinode (m, md, true, (m = m6 ⊃ mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m6]) ;mkdir(fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].meta, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, ∅) ) .nlink, (m = m6 ⊃ mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m6]) ;mkdir(fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].meta, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, ∅) ) .nsubdirs, (m = m6 ⊃ mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m6]) ;mkdir(fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].meta, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, ∅) ) .size)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 290:
(m6 = m ⊃ mkdir(m9, md, m7, m8, (∅)[str, m]);mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m])) = mkdir(m0, md0, m1, m2, entries), (m = m6 ⊃ mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m6]) ;mkdir(fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].meta, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, ∅) ) = mkdir(m3, md3, m4, m5, entries0), fs0[ri0[inodekey(m6)]] = inodenode(key0, md2, true, m7, m8, m9), fs0[ri0[dentrykey(m6, str)]] = dentrynode(key1, m), abs-children(m, fs0, ri0) = ∅, dentrykeys(inodekey(m), ri0) = ∅, fs0[ri0[inodekey(m)]].directory, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons (abs-dirs(fs0, ri0)[m6, mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m])] [m, (m = m6 ⊃ mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m6]) ;mkdir(fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].meta, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, ∅) ) .meta:= md ], abs-files(fs0, ri0)), 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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ], 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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ]), 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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ], 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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ], 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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ], 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 ≤ m8, 1 ≤ m9, fs0[ri0[inodekey(m)]].nlink = 1 → links(m, fs0, ri0) = ∅ ++ dentrykey(m6, str), boolvar4 → boolvar1, m7 ≠ 0 ∨ m6 = ROOT_INO, links(m6, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m6 = ROOT_INO ⊦ fs0[ri0[inodekey(m)]].nlink = 0, adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m = ROOT_INO, m = 0, m6 = 0, m8 = 0, m9 = 0, adr2 ∈ ri0 -- dentrykey(m6, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, abs-dirs(fs0, ri0)[m6, mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m])] [m, (m = m6 ⊃ mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m6]) ;mkdir(fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].meta, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, ∅) ) .meta:= md ] = abs-dirs (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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]) ∧ abs-files(fs0, ri0) = abs-files (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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]) ∧ orphans (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, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]) = orphans(fs0, ri0) ∧ mkinode(m6, md1, true, m7, m8, m9) = mkinode(m6, md0, true, m1, m2, m0) ∧ mkinode(m, md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) = mkinode(m, md, true, m4, m5, m3), 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] → [(m = m6 ⊃ mkdir (m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m6]) ;mkdir (fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].meta, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, ∅) ), m3, md3, m4, m5, entries0]

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: (m = m6 ⊃ mkdir(m9, md1, m7, m8, abs-children(m6, fs0, ri0)[str, m6]) ;mkdir (fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].meta, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, ∅) ), m3, md3, m4, m5, entries0