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Proof step 119 from proof refine-rename-overwrite-keep-parent-identity (previous step)

boolvar ↔ old_ino = new_ino, boolvar0 ↔ true, fs0[ri0[dentrykey(m6, str)]] = dentrynode(key1, m), fs0[ri0[inodekey(m6)]] = inodenode(key0, md2, true, m7, m8, m9), boolvar, dirs = abs-dirs(fs0, ri0)[old_ino, abs-dirs(fs0, ri0)[old_ino].entries:= (abs-dirs(fs0, ri0)[old_ino].entries -- str)], new_ino = m6, old_dent = mkdentry(str, m), old_ino = m6, 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(m6, str), 0)][adr2, dentrynode(dentrykey(m6, str), m)][adr3, inodenode(inodekey(m6), md1, true, m7, m8, m9)] [adr4, inodenode(inodekey(m), md, boolvar3, m0, m1, m2) ], 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, boolvar3, m0, m1, m2) ]), 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, boolvar3, m0, m1, m2) ], 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, boolvar3, m0, m1, m2) ], 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, boolvar3, m0, m1, m2) ], 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, fs0[ri0[inodekey(m)]].directory → dentrykeys(inodekey(m), ri0) = ∅, fs0[ri0[inodekey(m)]].directory → abs-children(m, fs0, ri0) = ∅, boolvar4 → boolvar1, m0 = 1 → links(m, fs0, ri0) = ∅ ++ dentrykey(m6, str), boolvar2 → 1 ≤ m8, fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m2 = fs0[ri0[inodekey(m)]].size ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar3 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar3, fs0[ri0[inodekey(m)]].directory ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m5 = fs0[ri0[inodekey(m)]].size ∧ m4 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar2 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m4 = 0 ∧ ¬ boolvar2, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar3 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar3 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri0[inodekey(m)]].size, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m4 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar2 ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m4 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m5 = fs0[ri0[inodekey(m)]].size, links(m6, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m6 = ROOT_INO, m7 ≠ 0 ∨ m6 = ROOT_INO ⊦ ⟨dirs[new_ino].entries[str] := old_dent.ino; new_dent := mkdentry(str, m); files := abs-files(fs0, ri0); 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#(mkinode(m6, md1, true, m7, m8, m9); dirs, files); afs_inode_sync#(mkinode(m6, md1, true, m7, m8, m9); dirs, files); new_child_inode := mkinode(m, md, boolvar3, m0, m1, m2); if boolvar0 then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := (new_child_inode.ino ∈ dirs ⊃ mkinode (new_child_inode.ino, dirs[new_child_inode.ino].meta, true, dirs[new_child_inode.ino].nlink, dirs[new_child_inode.ino].nsubdirs, dirs[new_child_inode.ino].size) ;mkinode (new_child_inode.ino, files[new_child_inode.ino].meta, false, files[new_child_inode.ino].nlink, 0, files[new_child_inode.ino].size) )}; old_inode := (m6 ∈ dirs ⊃ mkinode(m6, dirs[m6].meta, true, dirs[m6].nlink, dirs[m6].nsubdirs, dirs[m6].size) ;mkinode(m6, files[m6].meta, false, files[m6].nlink, 0, files[m6].size) ); new_inode := (m6 ∈ dirs ⊃ mkinode(m6, dirs[m6].meta, true, dirs[m6].nlink, dirs[m6].nsubdirs, dirs[m6].size) ;mkinode(m6, files[m6].meta, false, files[m6].nlink, 0, files[m6].size) ); err := ESUCCESS; asynced := ?⟩ ( afs-cons(dirs, files) → dirs = 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, boolvar3, m0, m1, m2) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]) ∧ files = 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, boolvar3, m0, m1, m2) ], 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, boolvar3, m0, m1, m2) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]) = orphans(fs0, ri0) ∧ (asynced → boolvar5) ∧ mkinode(m6, md1, true, m7, m8, m9) = old_inode ∧ mkinode(m6, md1, true, m7, m8, m9) = new_inode ∧ mkinode(m, md, boolvar3, m0, m1, m2) = new_child_inode ∧ negdentry(str) = old_dent ∧ mkdentry(str, m) = new_dent ∧ ESUCCESS = err), adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m = ROOT_INO, m = 0, m0 = 0, m6 = 0, m9 = 0, adr2 ∈ ri0 -- dentrykey(m6, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, m7 = 0 ∧ m6 ≠ ROOT_INO

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 120:
boolvar0 ↔ true, boolvar ↔ old_ino = new_ino, fs0[ri0[inodekey(m6)]] = inodenode(key0, md2, true, m7, m8, m9), fs0[ri0[dentrykey(m6, str)]] = dentrynode(key1, m), boolvar, dirs = dirs0[new_ino, dirs0[new_ino].entries:= dirs0[new_ino].entries[str, old_dent.ino]], dirs0 = abs-dirs(fs0, ri0)[old_ino, abs-dirs(fs0, ri0)[old_ino].entries:= (abs-dirs(fs0, ri0)[old_ino].entries -- str)], new_ino = m6, old_dent = mkdentry(str, m), old_ino = m6, old_dent.dentry?, orphans(fs0, ri0).inodes?, fo.inodes?, 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, boolvar3, m0, m1, m2) ], 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, boolvar3, m0, m1, m2) ]), 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, boolvar3, m0, m1, m2) ], 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, boolvar3, m0, m1, m2) ], 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, boolvar3, m0, m1, m2) ], 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 ≤ m9, boolvar2 → 1 ≤ m8, m0 = 1 → links(m, fs0, ri0) = ∅ ++ dentrykey(m6, str), boolvar4 → boolvar1, fs0[ri0[inodekey(m)]].directory → abs-children(m, fs0, ri0) = ∅, fs0[ri0[inodekey(m)]].directory → dentrykeys(inodekey(m), ri0) = ∅, m7 ≠ 0 ∨ m6 = ROOT_INO, links(m6, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m6 = ROOT_INO, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m4 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar2 ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m4 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m5 = fs0[ri0[inodekey(m)]].size, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar3 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar3 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m)]].directory ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m5 = fs0[ri0[inodekey(m)]].size ∧ m4 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar2 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m3 = fs0[ri0[inodekey(m)]].nlink ∧ m4 = 0 ∧ ¬ boolvar2, fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m2 = fs0[ri0[inodekey(m)]].size ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar3 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar3 ⊦ ⟨new_dent := mkdentry(str, m); files := abs-files(fs0, ri0); 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#(mkinode(m6, md1, true, m7, m8, m9); dirs, files); afs_inode_sync#(mkinode(m6, md1, true, m7, m8, m9); dirs, files); new_child_inode := mkinode(m, md, boolvar3, m0, m1, m2); if boolvar0 then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := (new_child_inode.ino ∈ dirs ⊃ mkinode (new_child_inode.ino, dirs[new_child_inode.ino].meta, true, dirs[new_child_inode.ino].nlink, dirs[new_child_inode.ino].nsubdirs, dirs[new_child_inode.ino].size) ;mkinode (new_child_inode.ino, files[new_child_inode.ino].meta, false, files[new_child_inode.ino].nlink, 0, files[new_child_inode.ino].size) )}; old_inode := (m6 ∈ dirs ⊃ mkinode(m6, dirs[m6].meta, true, dirs[m6].nlink, dirs[m6].nsubdirs, dirs[m6].size) ;mkinode(m6, files[m6].meta, false, files[m6].nlink, 0, files[m6].size) ); new_inode := (m6 ∈ dirs ⊃ mkinode(m6, dirs[m6].meta, true, dirs[m6].nlink, dirs[m6].nsubdirs, dirs[m6].size) ;mkinode(m6, files[m6].meta, false, files[m6].nlink, 0, files[m6].size) ); err := ESUCCESS; asynced := ?⟩ ( afs-cons(dirs, files) → dirs = 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, boolvar3, m0, m1, m2) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]) ∧ files = 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, boolvar3, m0, m1, m2) ], 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, boolvar3, m0, m1, m2) ], ri0[dentrykey(m6, str), adr2][inodekey(m6), adr3][inodekey(m), adr4]) = orphans(fs0, ri0) ∧ (asynced → boolvar5) ∧ mkinode(m6, md1, true, m7, m8, m9) = old_inode ∧ mkinode(m6, md1, true, m7, m8, m9) = new_inode ∧ mkinode(m, md, boolvar3, m0, m1, m2) = new_child_inode ∧ negdentry(str) = old_dent ∧ mkdentry(str, m) = new_dent ∧ ESUCCESS = err), adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m = ROOT_INO, m0 = 0, m6 = 0, m9 = 0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m6, str), m7 = 0 ∧ m6 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)