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Proof step 99 from proof refine-rename-overwrite-keep-parent-identity (previous step)

fs0[ri0[inodekey(m6)]] = inodenode(key0, md2, true, m7, m8, m9), fs0[ri0[dentrykey(m6, str)]] = dentrynode(key1, m), dirs = abs-dirs(fs0, ri0), err = err0, files = abs-files(fs0, ri0), new_child_inode = new_dent_inode, new_dent = old_dent2, new_dent_inode = mkinode(m, md, boolvar3, m0, m1, m2), new_inode = mkinode(m6, md1, true, m7, m8, m9), new_parent_inode = new_inode, old_child_inode = old_dent_inode, old_dent = old_dent1, old_dent1 = mkdentry(str, m), old_dent2 = mkdentry(str, m), old_dent_inode = mkinode(m, md0, boolvar2, m3, m4, m5), old_inode = mkinode(m6, md1, true, m7, m8, m9), 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(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)), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files), 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 ⊦ ⟨ 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 := ?⟩ ( 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 → boolvar0) ∧ mkinode(m6, md1, true, m7, m8, m9) = old_parent_inode ∧ mkinode(m6, md1, true, m7, m8, m9) = new_parent_inode ∧ mkinode(m, md0, boolvar2, m3, m4, m5) = old_child_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 or right

And obtained the following new goals

Rule argument

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