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Proof step 108 from proof refine-rename-overwrite-keep-parent-different (previous step)

¬ fs0[ri0[inodekey(m3)]].directory ↔ ¬ fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m7)]] = inodenode(key1, md2, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), fs0[ri0[dentrykey(m7, str)]] = dentrynode(key2, m), fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m3), dirs = abs-dirs(fs0, ri0), files = abs-files(fs0, ri0), links(m3, fs0, ri0) = ∅ ++ dentrykey(m7, str0), new_dent_inode = mkinode(m3, md0, boolvar2, 1, m5, m6), new_inode = mkinode(m7, md1, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), old_dent0 = mkdentry(str, m), old_dent1 = mkdentry(str0, m3), old_dent_inode = mkinode(m, md, boolvar1, m0, m1, m2), old_inode = mkinode(m7, md1, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), adr1 ≠ adr2, adr1 ≠ adr3, adr1 ≠ adr4, adr2 ≠ adr3, adr2 ≠ adr4, adr3 ≠ adr4, m3 ≠ ROOT_INO, m3 ≠ 0, m7 ≠ 0, mkdentry(str, m) ≠ mkdentry(str0, m3), 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(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ri-inj((ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), inodekey(m) ∈ ri0, inodekey(m3) ∈ ri0, dentrykey(m7, str) ∈ ri0, dentrykey(m7, str0) ∈ ri0, inodekey(m7) ∈ ri0, ri0[dentrykey(m7, str0)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[dentrykey(m7, str)] ∈ fs0, ¬ adr4 ∈ (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3], ¬ adr2 ∈ ri0 -- dentrykey(m7, str), ¬ adr4 ∈ fs0, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ adr3 ∈ (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2], boolvar3 → boolvar4, fs0[ri0[inodekey(m3)]].directory → abs-children(m3, fs0, ri0) = ∅, fs0[ri0[inodekey(m3)]].directory → dentrykeys(inodekey(m3), ri0) = ∅, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∨ fs0[ri0[inodekey(m3)]].directory ∧ boolvar2 ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∧ m6 = fs0[ri0[inodekey(m3)]].size, fs0[ri0[inodekey(m3)]].directory ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m6 = fs0[ri0[inodekey(m3)]].size ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∧ boolvar2 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = 0 ∧ ¬ boolvar2, m4 ≠ 0 ∨ m7 = ROOT_INO, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m2 = fs0[ri0[inodekey(m)]].size ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar1 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1 ⊦ ⟨afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar3)⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]) ∧ files = abs-files (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]) ∧ orphans (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]) = orphans(fs0, ri0) ++ inodekey(m3) ∧ (boolvar3 → boolvar0) ∧ mkinode(m7, md1, true, m4, n0, m11) = old_inode ∧ mkinode(m7, md1, true, m4, n0, m11) = new_inode ∧ mkinode(m, md, boolvar1, m0, m1, m2) = old_dent_inode ∧ mkinode(m3, md0, boolvar2, 0, m5, m6) = new_dent_inode ∧ negdentry(str) = old_dent0 ∧ mkdentry(str0, m) = old_dent1 ∧ ESUCCESS = err0), m4 = 0 ∧ m7 ≠ ROOT_INO

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 109:
¬ fs0[ri0[inodekey(m3)]].directory ↔ ¬ fs0[ri0[inodekey(m)]].directory, fs0[ri0[dentrykey(m7, str0)]] = dentrynode(key0, m3), fs0[ri0[dentrykey(m7, str)]] = dentrynode(key2, m), fs0[ri0[inodekey(m7)]] = inodenode(key1, md2, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), dirs = abs-dirs(fs0, ri0), err = err0, files = abs-files(fs0, ri0), links(m3, fs0, ri0) = ∅ ++ dentrykey(m7, str0), new_child_inode = new_dent_inode, new_dent = old_dent1, new_dent_inode = mkinode(m3, md0, boolvar2, 1, m5, m6), new_inode = mkinode(m7, md1, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), new_parent_inode = new_inode, old_child_inode = old_dent_inode, old_dent = old_dent0, old_dent0 = mkdentry(str, m), old_dent1 = mkdentry(str0, m3), old_dent_inode = mkinode(m, md, boolvar1, m0, m1, m2), old_inode = mkinode(m7, md1, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), old_parent_inode = old_inode, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3), 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(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)][adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11)] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4], orphans(fs0, ri0) ++ inodekey(m3), fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri0[dentrykey(m7, str)] ∈ fs0, ri0[inodekey(m7)] ∈ fs0, ri0[dentrykey(m7, str0)] ∈ fs0, inodekey(m7) ∈ ri0, dentrykey(m7, str0) ∈ ri0, dentrykey(m7, str) ∈ ri0, inodekey(m3) ∈ ri0, inodekey(m) ∈ ri0, fs0[ri0[inodekey(m3)]].directory → dentrykeys(inodekey(m3), ri0) = ∅, fs0[ri0[inodekey(m3)]].directory → abs-children(m3, fs0, ri0) = ∅, boolvar3 → boolvar4, fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m2 = fs0[ri0[inodekey(m)]].size ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar1 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri0[inodekey(m)]].size, links(m7, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m7 = ROOT_INO, fs0[ri0[inodekey(m3)]].directory ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m6 = fs0[ri0[inodekey(m3)]].size ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∧ boolvar2 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = 0 ∧ ¬ boolvar2, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∨ fs0[ri0[inodekey(m3)]].directory ∧ boolvar2 ∧ 1 = fs0[ri0[inodekey(m3)]].nlink ∧ m5 = fs0[ri0[inodekey(m3)]].nsubdirs ∧ m6 = fs0[ri0[inodekey(m3)]].size ⊦ ⟨if pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) then { let old_ino = old_parent_inode.ino, new_ino = new_parent_inode.ino, boolvar0 = new_dent.dentry? in let boolvar = old_ino = new_ino ∧ new_dent = old_dent in {dirs[old_ino].entries := dirs[old_ino].entries -- old_dent.name; if ¬ boolvar then {dirs[old_ino].size := dirs[old_ino].size - 1; if old_dent.ino ∈ dirs then dirs[old_ino].nsubdirs := dirs[old_ino].nsubdirs - 1}; dirs[new_ino].entries[new_dent.name] := old_dent.ino; if boolvar0 ∧ ¬ boolvar then let ino = new_dent.ino in afs_drop_nlink#(ino; dirs, files); if ¬ boolvar0 then {dirs[new_ino].size := dirs[new_ino].size + 1; if old_dent.ino ∈ dirs then dirs[new_ino].nsubdirs := dirs[new_ino].nsubdirs + 1}; new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(old_parent_inode; dirs, files); afs_inode_sync#(new_parent_inode; dirs, files); if boolvar0 then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := getinode(new_child_inode.ino, dirs, files)}; old_parent_inode := getinode(old_parent_inode.ino, dirs, files); new_parent_inode := getinode(new_parent_inode.ino, dirs, files); err := ESUCCESS} or fail#(; ; err); asynced := ?} else abort⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]) ∧ files = abs-files (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]) ∧ orphans (fs0[adr1, dentrynode(dentrykey(m7, str), 0)][adr2, dentrynode(dentrykey(m7, str0), m)] [adr3, inodenode(inodekey(m7), md1, true, m4, n0, m11) ] [adr4, inodenode(inodekey(m3), md0, boolvar2, 0, m5, m6) ], (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3][inodekey(m3), adr4]) = orphans(fs0, ri0) ++ inodekey(m3) ∧ (asynced → boolvar0) ∧ mkinode(m7, md1, true, m4, n0, m11) = old_parent_inode ∧ mkinode(m7, md1, true, m4, n0, m11) = new_parent_inode ∧ mkinode(m, md, boolvar1, m0, m1, m2) = old_child_inode ∧ mkinode(m3, md0, boolvar2, 0, m5, m6) = new_child_inode ∧ negdentry(str) = old_dent ∧ mkdentry(str0, m) = new_dent ∧ ESUCCESS = err), adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m3 = ROOT_INO, m3 = 0, m7 = 0, mkdentry(str, m) = mkdentry(str0, m3), adr4 ∈ (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2][inodekey(m7), adr3], adr2 ∈ ri0 -- dentrykey(m7, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ (ri0 -- dentrykey(m7, str))[dentrykey(m7, str0), adr2], m4 = 0 ∧ m7 ≠ ROOT_INO

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_rename# (; OLD_PARENT_INODE, NEW_PARENT_INODE, OLD_CHILD_INODE, NEW_CHILD_INODE, OLD_DENT, NEW_DENT, ERR, DIRS, FILES ; ASYNCED ) {if pre-rename (OLD_PARENT_INODE, OLD_DENT, OLD_CHILD_INODE, NEW_PARENT_INODE, NEW_DENT, NEW_CHILD_INODE, DIRS, FILES) then { let OLD_INO = OLD_PARENT_INODE.ino, NEW_INO = NEW_PARENT_INODE.ino, OVERWRITE = NEW_DENT.dentry? in let IDENTITY = OLD_INO = NEW_INO ∧ NEW_DENT = OLD_DENT in {DIRS[OLD_INO].entries := DIRS[OLD_INO].entries -- OLD_DENT.name; if ¬ IDENTITY then {DIRS[OLD_INO].size := DIRS[OLD_INO].size - 1; if OLD_DENT.ino ∈ DIRS then DIRS[OLD_INO].nsubdirs := DIRS[OLD_INO].nsubdirs - 1}; DIRS[NEW_INO].entries[NEW_DENT.name] := OLD_DENT.ino; if OVERWRITE ∧ ¬ IDENTITY then let INO = NEW_DENT.ino in afs_drop_nlink#(INO; DIRS, FILES); if ¬ OVERWRITE then {DIRS[NEW_INO].size := DIRS[NEW_INO].size + 1; if OLD_DENT.ino ∈ DIRS then DIRS[NEW_INO].nsubdirs := DIRS[NEW_INO].nsubdirs + 1}; NEW_DENT := mkdentry(NEW_DENT.name, OLD_DENT.ino); OLD_DENT := negdentry(OLD_DENT.name); afs_inode_sync#(OLD_PARENT_INODE; DIRS, FILES); afs_inode_sync#(NEW_PARENT_INODE; DIRS, FILES); if OVERWRITE then {afs_inode_sync#(NEW_CHILD_INODE; DIRS, FILES); NEW_CHILD_INODE := getinode(NEW_CHILD_INODE.ino, DIRS, FILES)}; OLD_PARENT_INODE := getinode(OLD_PARENT_INODE.ino, DIRS, FILES); NEW_PARENT_INODE := getinode(NEW_PARENT_INODE.ino, DIRS, FILES); ERR := ESUCCESS} or fail#(; ; ERR); ASYNCED := ?} else abort };