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Proof step 141 from proof refine-rename-overwrite-reparent-file (previous step)

boolvar0 ↔ true, boolvar ↔ old_ino = new_ino ∧ mkdentry(str0, m0) = mkdentry(str, m), 0 = fs0[ri0[inodekey(m0)]].nsubdirs, 1 = fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m)]] = inodenode(key, md5, false, fs0[ri0[inodekey(m)]].nlink, 0, m12), fs0[ri0[inodekey(m4)]] = inodenode(key2, md4, true, m6, m7, m8), fs0[ri0[dentrykey(m4, str0)]] = dentrynode(key0, m0), fs0[ri0[dentrykey(m9, str)]] = dentrynode(key3, m), fs0[ri0[inodekey(m9)]] = inodenode(key1, md3, true, m1, m3, m14 + 1), ¬ boolvar, dirs = dirs1[new_ino, dirs1[new_ino].entries:= dirs1[new_ino].entries[str0, 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)], dirs1 = dirs0[old_ino, dirs0[old_ino].size:= (dirs0[old_ino].size - 1)], files = abs-files(fs0, ri0), ino = new_dent.ino, links(m0, fs0, ri0) = ∅ ++ dentrykey(m4, str0), new_dent = mkdentry(str0, m0), new_ino = m4, old_dent = mkdentry(str, m), old_ino = m9, new_dent.dentry?, 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(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)][adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14)] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, 0, 0, m5) ], (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4][inodekey(m0), adr5]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)][adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14)] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, 0, 0, m5) ]), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, dentrynode(dentrykey(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)][adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14)] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, 0, 0, m5) ], (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0)), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)][adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14)] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, 0, 0, m5) ], (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0), 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(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4][inodekey(m0), adr5]), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)][adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14)] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, 0, 0, m5) ], (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4][inodekey(m0), adr5], orphans(fs0, ri0) ++ inodekey(m0), fi, fo, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri0[dentrykey(m9, str)] ∈ fs0, ri0[inodekey(m9)] ∈ fs0, ri0[inodekey(m4)] ∈ fs0, ri0[dentrykey(m4, str0)] ∈ fs0, inodekey(m4) ∈ ri0, inodekey(m9) ∈ ri0, dentrykey(m4, str0) ∈ ri0, inodekey(m0) ∈ ri0, dentrykey(m9, str) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, dirs0[old_ino].size ≥ 1, boolvar2 → boolvar3, m6 ≠ 0 ∨ m4 = ROOT_INO, m1 ≠ 0 ∨ m9 = ROOT_INO, links(m4, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m4 = ROOT_INO, links(m9, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m9 = ROOT_INO ⊦ ⟨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(m9, md2, true, m1, m3, m14 + 1); dirs, files); afs_inode_sync#(mkinode(m4, md1, true, m6, m7, m8); dirs, files); new_child_inode := mkinode(m0, md0, false, 1, 0, m5); 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 := (m9 ∈ dirs ⊃ mkinode(m9, dirs[m9].meta, true, dirs[m9].nlink, dirs[m9].nsubdirs, dirs[m9].size) ;mkinode(m9, files[m9].meta, false, files[m9].nlink, 0, files[m9].size) ); new_inode := (m4 ∈ dirs ⊃ mkinode(m4, dirs[m4].meta, true, dirs[m4].nlink, dirs[m4].nsubdirs, dirs[m4].size) ;mkinode(m4, files[m4].meta, false, files[m4].nlink, 0, files[m4].size) ); err := ESUCCESS; asynced := ?⟩ ( afs-cons(dirs, files) → dirs = abs-dirs (fs0[adr1, dentrynode(dentrykey(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)] [adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14) ] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, 0, 0, m5) ], (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4][inodekey(m0), adr5]) ∧ files = abs-files (fs0[adr1, dentrynode(dentrykey(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)] [adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14) ] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, 0, 0, m5) ], (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4][inodekey(m0), adr5]) ∧ orphans (fs0[adr1, dentrynode(dentrykey(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)] [adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14) ] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, 0, 0, m5) ], (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4][inodekey(m0), adr5]) = orphans(fs0, ri0) ++ inodekey(m0) ∧ (asynced → boolvar1) ∧ mkinode(m9, md2, true, m1, m3, m14) = old_inode ∧ mkinode(m4, md1, true, m6, m7, m8) = new_inode ∧ mkinode(m0, md0, false, 0, 0, m5) = new_child_inode ∧ negdentry(str) = old_dent ∧ mkdentry(str0, m) = new_dent ∧ ESUCCESS = err), 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, m4 = 0, m9 = m4, m9 = 0, fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(m)]].directory, adr4 ∈ (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3], adr2 ∈ ri0 -- dentrykey(m9, str), adr5 ∈ fs0, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2], adr5 ∈ (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4], old_dent.ino ∈ dirs1, m1 = 0 ∧ m9 ≠ ROOT_INO, m6 = 0 ∧ m4 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)% ⊦ m + 1 ≠ 0; (s)%⊦ mkdir(m, md, m0, m1, entries).size:= m2 = mkdir(m2, md, m0, m1, entries); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).meta = md; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ mkdentry(str, m).name = str; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ (ad.entries:= entries).size = ad.size; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)%⊦ mkdir(m, md, m0, m1, entries).entries:= entries0 = mkdir(m, md, m0, m1, entries0); (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)