[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 138 from proof refine-mkdir (previous step)

fs1[ri1[inodekey(ino)]] = inodenode(key0, md1, true, m1, m2, m6), (abs-dirs(fs1, ri1)[ino, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(ino, fs1, ri1)[str, n])] ++ n)[ino] = mkdir(m, md0, m3, m4, entries), orphans(fs1, ri1).inodes?, fo.inodes?, afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), afs-cons ((abs-dirs(fs1, ri1)[ino, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(ino, fs1, ri1)[str, n])] ++ n)[n, mkdir(0, md, 1, 0, ∅)] [ino, mkdir(m, md2, m3, m4, entries) ], abs-files(fs1, ri1)), file-node-cons (fs1[adr1, inodenode(inodekey(ino), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3]), file-node-cons(fs1, ri1), log-cons (log0, fs1[adr1, inodenode(inodekey(ino), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ]), log-cons(log0, fs1), orphans-cons (fs1[adr1, inodenode(inodekey(ino), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3], orphans(fs1, ri1)), orphans-cons(fs1, ri1, orphans(fs1, ri1)), replay-cons-strong (fs1[adr1, inodenode(inodekey(ino), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ri-inj(ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3]), ri-inj(ri1), ri-inj(fi), ubifs-cons (fs1[adr1, inodenode(inodekey(ino), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), inodekey(ino) ∈ ri1, ri1[inodekey(ino)] ∈ fs1, asynced0 → boolvar0, links(ino, abs-dirs(fs1, ri1)) ≠ ∅ ∨ ino = ROOT_INO, m1 ≠ 0 ∨ ino = ROOT_INO ⊦ adr1 = adr3, adr2 = adr3, adr2 = adr1, ino = 0, mkdir(m, md2, m3, m4, entries) = mkdir (m6 + 1, md2, m1, m2 + 1, abs-children (ino, fs1[adr1, inodenode(inodekey(ino), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3])), n = 0, adr3 ∈ fs1, adr2 ∈ fs1, adr1 ∈ fs1, inodekey(n) ∈ ri1, inodekey(n) ∈ fo, dentrykey(ino, str) ∈ ri1, m1 = 0 ∧ ino ≠ ROOT_INO

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 139:
ino ∈ dirs, ino0 ≠ 0, ¬ ino0 ∈ dirs ⊦ ino ≠ ino0 → (dirs ++ ino0)[ino] = dirs[ino]
Proof step 140:
abs-dirs(fs1, ri1)[ino, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(ino, fs1, ri1)[str, n])][ino] = mkdir(m, md0, m3, m4, entries), fs1[ri1[inodekey(ino)]] = inodenode(key0, md1, true, m1, m2, m6), fo.inodes?, orphans(fs1, ri1).inodes?, afs-cons ((abs-dirs(fs1, ri1)[ino, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(ino, fs1, ri1)[str, n])] ++ n)[n, mkdir(0, md, 1, 0, ∅)] [ino, mkdir(m, md2, m3, m4, entries) ], abs-files(fs1, ri1)), afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), file-node-cons(fs1, ri1), file-node-cons (fs1[adr1, inodenode(inodekey(ino), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3]), log-cons(log0, fs1), log-cons (log0, fs1[adr1, inodenode(inodekey(ino), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ]), orphans-cons(fs1, ri1, orphans(fs1, ri1)), orphans-cons (fs1[adr1, inodenode(inodekey(ino), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3], orphans(fs1, ri1)), replay-cons-strong(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), replay-cons-strong (fs1[adr1, inodenode(inodekey(ino), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri1), ri-inj(ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3]), ubifs-cons(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ubifs-cons (fs1[adr1, inodenode(inodekey(ino), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri1[inodekey(ino)] ∈ fs1, inodekey(ino) ∈ ri1, ino ∈ abs-dirs(fs1, ri1)[ino, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(ino, fs1, ri1)[str, n])], asynced0 → boolvar0, m1 ≠ 0 ∨ ino = ROOT_INO, links(ino, abs-dirs(fs1, ri1)) ≠ ∅ ∨ ino = ROOT_INO ⊦ adr1 = adr3, adr2 = adr1, adr2 = adr3, ino = 0, ino = n, mkdir(m, md2, m3, m4, entries) = mkdir (m6 + 1, md2, m1, m2 + 1, abs-children (ino, fs1[adr1, inodenode(inodekey(ino), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(ino, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri1[inodekey(ino), adr1][dentrykey(ino, str), adr2][inodekey(n), adr3])), n = 0, dentrykey(ino, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, n ∈ abs-dirs(fs1, ri1)[ino, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(ino, fs1, ri1)[str, n])], m1 = 0 ∧ ino ≠ ROOT_INO

Rule argument

spec: heap, inst: dir-heap name: at-alloc seq: ino ∈ dirs, ino0 ≠ 0, ¬ ino0 ∈ dirs ⊦ ino ≠ ino0 → (dirs ++ ino0)[ino] = dirs[ino] subst: [ino, ino0, dirs] → [ino, n, abs-dirs(fs1, ri1) [ino, mkdir (m6 + 1, md1, m1, m2 + 1, abs-children(ino, fs1, ri1)[str, n]) ]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s) Used terms: ino, n, abs-dirs(fs1, ri1) [ino, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(ino, fs1, ri1)[str, n]) ]