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Proof step 87 from proof refine-link (previous step)

fs0[ri0[dentrykey(ino1, str)]].ino = fs0[ri0[dentrykey(ino, str)]].ino, fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m0, m1, m2), fs0[ri0[dentrykey(ino0, str)]] = dentrynode(key, fs0[ri0[dentrykey(ino, str)]].ino), fs0[ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)]] = inodenode(key1, md2, false, m3, 0, m5), dirs = abs-dirs(fs0, ri0), files = abs-files(fs0, ri0), old_dent0 = negdentry(str0), p_inode0 = mkinode(m, md, true, m0, m1, m2), p_inode1 = mkinode(fs0[ri0[dentrykey(ino, str)]].ino, md0, false, m3, 0, m6), fs0[ri0[dentrykey(ino, str)]].ino ≠ 0, adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, m ≠ 0, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(ino1)]].directory, fs0[ri0[inodekey(ino)]].directory, orphans(fs0, ri0).inodes?, fo.inodes?, 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, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3], orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ri-inj(ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(ino0) ∈ ri0, inodekey(ino1) ∈ ri0, inodekey(ino) ∈ ri0, dentrykey(ino1, str) ∈ ri0, dentrykey(ino, str) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(ino, str)]].ino)] ∈ fs0, inodekey(fs0[ri0[dentrykey(ino, str)]].ino) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, dentrykey(ino0, str) ∈ ri0, ¬ dentrykey(m, str0) ∈ ri0, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, asynced → boolvar0, links(fs0[ri0[dentrykey(ino, str)]].ino, abs-dirs(fs0, ri0)) ≠ ∅ ∨ fs0[ri0[dentrykey(ino, str)]].ino = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, links(ino0, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino0 = ROOT_INO, m0 ≠ 0 ∨ m = ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, m3 ≠ 0 ∨ fs0[ri0[dentrykey(ino, str)]].ino = ROOT_INO ⊦ ⟨afs_link#(mkdentry(str, fs0[ri0[dentrykey(ino, str)]].ino); p_inode0, p_inode1, old_dent0, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3]) ∧ files = abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3]) ∧ orphans (abs-dirs (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3]), abs-files (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino, str)]].ino), adr3])) = abs-keys(orphans(fs0, ri0)) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m0, m1, m2 + 1) = p_inode0 ∧ mkinode(fs0[ri0[dentrykey(ino, str)]].ino, md0, false, m3 + 1, 0, m6) = p_inode1 ∧ mkdentry(str0, fs0[ri0[dentrykey(ino, str)]].ino) = old_dent0 ∧ ESUCCESS = err0), fs0[ri0[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO, m0 = 0 ∧ m ≠ ROOT_INO, m3 = 0 ∧ fs0[ri0[dentrykey(ino, str)]].ino ≠ ROOT_INO

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: afs-asm name: inv-link seq: afs-cons(dirs, files), pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files) ⊦ ⟪afs_link# (old_dent ; p_inode, c_inode, new_dent, err, dirs, files ; asynced)⟫ afs-cons(dirs, files) subst: [old_dent, files, dirs, err, new_dent, c_inode, p_inode, asynced] → [mkdentry(str, fs0[ri0[dentrykey(ino, str)]].ino), files, dirs, err0, old_dent0, p_inode1, p_inode0, asynced] flags: List([[1,0,0]])

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