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Proof step 764 from proof refine-rename-overwrite-reparent-dir (previous step)

m14 + 1 = fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m)]] = inodenode(key, md6, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size), 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(m0)]] = inodenode(key3, md5, true, m14 + 1, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size), abs-children(m0, fs0, ri0) = ∅, dentrykeys(inodekey(m0), ri0) = ∅, dirs = abs-dirs(fs0, ri0)[m11, mkdir(m13, md4, m4, m16, abs-children(m11, fs0, ri0) -- str)] [m7, abs-dirs(fs0, ri0)[m7].entries:= abs-dirs(fs0, ri0)[m7].entries[str0, m] ], files = abs-files(fs0, ri0), 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, m14 ≠ 0, m7 ≠ 0, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m0)]].directory, 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, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]), 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, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ]), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), 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, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0)), 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, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0), fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj((ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]), ri-inj(fi), ri-inj(ri0), 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, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5], orphans(fs0, ri0), fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), 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, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ 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 → boolvar3, 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_drop_nlink#(mkdentry(str0, m0).ino; dirs, files); old_dent := mkdentry(str, m); boolvar0 := true; if ¬ boolvar0 then {dirs[m7].size := dirs[m7].size + 1; if old_dent.ino ∈ dirs then dirs[m7].nsubdirs := dirs[m7].nsubdirs + 1}; new_dent := mkdentry(str0, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(mkinode(m11, md2, true, m4, m16 + 1, m13 + 1); dirs, files); afs_inode_sync#(mkinode(m7, md1, true, m1, m2, m3); dirs, files); new_child_inode := mkinode(m0, md0, true, m14 + 1, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size); 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 := (m11 ∈ dirs ⊃ mkinode(m11, dirs[m11].meta, true, dirs[m11].nlink, dirs[m11].nsubdirs, dirs[m11].size) ;mkinode(m11, files[m11].meta, false, files[m11].nlink, 0, files[m11].size) ); new_inode := (m7 ∈ dirs ⊃ mkinode(m7, dirs[m7].meta, true, dirs[m7].nlink, dirs[m7].nsubdirs, dirs[m7].size) ;mkinode(m7, files[m7].meta, false, files[m7].nlink, 0, files[m7].size) ); err := ESUCCESS; asynced := ?⟩ ( afs-cons(dirs, files) → 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, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (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, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]) ∧ orphans (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, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) ], (ri0 -- dentrykey(m11, str))[dentrykey(m7, str0), adr2][inodekey(m11), adr3][inodekey(m7), adr4][inodekey(m0), adr5]) = orphans(fs0, ri0) ∧ (asynced → boolvar1) ∧ mkinode(m11, md2, true, m4, m16, m13) = old_inode ∧ mkinode(m7, md1, true, m1, m2, m3) = new_inode ∧ mkinode(m0, md0, true, m14, fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m0)]].size) = new_child_inode ∧ negdentry(str) = old_dent ∧ mkdentry(str0, m) = new_dent ∧ ESUCCESS = err), m1 = 0 ∧ m7 ≠ ROOT_INO, m4 = 0 ∧ m11 ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [abs-dirs(fs0, ri0)[m7], m5, md, m6, m8, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: abs-dirs(fs0, ri0)[m7], m5, md, m6, m8, entries