[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 114 from proof refine-rename-overwrite-reparent-dir (previous step)

fs0[ri0[inodekey(m0)]] = inodenode(key3, md5, true, 1, m6, m8), fs0[ri0[inodekey(m11)]] = inodenode(key2, md4, true, m4, m16 + 1, m13 + 1), fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m0), fs0[ri0[dentrykey(m11, str)]] = dentrynode(key4, m), fs0[ri0[inodekey(m7)]] = inodenode(key1, md3, true, m1, m2, m3), fs0[ri0[inodekey(m)]] = inodenode(key, md6, true, m5, m9, m10), abs-children(m0, fs0, ri0) = ∅, dentrykeys(inodekey(m0), ri0) = ∅, dirs = abs-dirs(fs0, ri0), files = abs-files(fs0, ri0), links(m0, fs0, ri0) = ∅ ++ dentrykey(m7, str0), new_dent_inode = mkinode(m0, md0, true, 1, m6, m8), new_inode = mkinode(m7, md1, true, m1, m2, m3), old_dent0 = mkdentry(str, m), old_dent1 = mkdentry(str0, m0), old_dent_inode = mkinode(m, md, true, m5, m9, m10), old_inode = mkinode(m11, md2, true, m4, m16 + 1, m13 + 1), adr1 ≠ adr2, adr1 ≠ adr3, adr1 ≠ adr4, adr1 ≠ adr5, adr2 ≠ adr3, adr2 ≠ adr4, adr2 ≠ adr5, adr3 ≠ adr4, adr3 ≠ adr5, adr4 ≠ adr5, m0 ≠ ROOT_INO, m0 ≠ 0, m11 ≠ m7, m11 ≠ 0, m7 ≠ 0, 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(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, m6, m8) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, m6, m8) ]), orphans-cons (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, m6, m8) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, m6, m8) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0), fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ri-inj((ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13)] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, m6, m8) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0), fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, ri0[dentrykey(m11, str)] ∈ fs0, ri0[inodekey(m11)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, ri0[dentrykey(m7, str0)] ∈ fs0, inodekey(m11) ∈ ri0, inodekey(m7) ∈ ri0, dentrykey(m11, str) ∈ ri0, inodekey(m0) ∈ ri0, dentrykey(m7, str0) ∈ ri0, ¬ adr4 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3], ¬ adr2 ∈ ri0 -- dentrykey(m11, str), ¬ adr5 ∈ fs0, ¬ adr4 ∈ fs0, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ adr3 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2], ¬ adr5 ∈ (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4], boolvar2 → boolvar0, m4 ≠ 0 ∨ m11 = ROOT_INO, m1 ≠ 0 ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m11 = ROOT_INO, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO ⊦ ⟨afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar2)⟩ ( dirs = abs-dirs (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13) ] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, m6, m8) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]) ∧ files = abs-files (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13) ] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, m6, m8) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]) ∧ orphans (abs-dirs (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13) ] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, m6, m8) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]), abs-files (fs0[adr1, dentrynode(dentrykey(m11, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m11), md2, true, m4, m16, m13) ] [adr4, inodenode(inodekey(m7), md1, true, m1, m2, m3) ] [adr5, inodenode(inodekey(m0), md0, true, 0, m6, m8) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5])) = abs-keys(orphans(fs0, ri0)) ++ m0 ∧ (boolvar2 → boolvar1) ∧ mkinode(m11, md2, true, m4, m16, m13) = old_inode ∧ mkinode(m7, md1, true, m1, m2, m3) = new_inode ∧ mkinode(m, md, true, m5, m9, m10) = old_dent_inode ∧ mkinode(m0, md0, true, 0, m6, m8) = new_dent_inode ∧ negdentry(str) = old_dent0 ∧ mkdentry(str0, m) = old_dent1 ∧ ESUCCESS = err0), m1 = 0 ∧ m7 ≠ ROOT_INO, m4 = 0 ∧ m11 ≠ ROOT_INO

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: afs-asm name: inv-renam seq: afs-cons(dirs, files), pre-rename (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) ⊦ ⟪afs_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files ; asynced)⟫ afs-cons(dirs, files) subst: [files, dirs, err, new_dent, old_dent, new_child_inode, old_child_inode, new_parent_inode, old_parent_inode, asynced] → [files, dirs, err0, old_dent1, old_dent0, new_dent_inode, old_dent_inode, new_inode, old_inode, boolvar2] flags: List([[1,0,0]])

Additional information