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Proof step 1153 from proof refine-rename-overwrite-keep-parent-different (previous step)

¬ fs[ri[inodekey(m3)]].directory ↔ ¬ fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m7)]] = inodenode(key1, md2, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), fs[ri[dentrykey(m7, str)]] = dentrynode(key, m), fs[ri[dentrykey(m7, str0)]] = dentrynode(key0, m3), dirs = abs-dirs(fs, ri), err = err1, files = abs-files(fs, ri), new_child_inode = new_dent_inode, new_dent = old_dent1, new_dent_inode = mkinode(m3, md0, boolvar2, m10 + 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, fo.inodes?, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-cons(ri, fs), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m7, str) ∈ ri, ri[dentrykey(m7, str)] ∈ fs, inodekey(m7) ∈ ri, ri[inodekey(m7)] ∈ fs, inodekey(m) ∈ ri, inodekey(m3) ∈ ri, ri[dentrykey(m7, str0)] ∈ fs, dentrykey(m7, str0) ∈ ri, ⌊err0⌋ , m10 = 0 → links(m3, fs, ri) = ∅ ++ dentrykey(m7, str0), boolvar3 → boolvar4, fs[ri[inodekey(m3)]].directory → abs-children(m3, fs, ri) = ∅, fs[ri[inodekey(m3)]].directory → dentrykeys(inodekey(m3), ri) = ∅, m4 ≠ 0 ∨ m7 = ROOT_INO, links(m7, abs-dirs(fs, ri)) ≠ ∅ ∨ m7 = ROOT_INO, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar1 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∨ fs[ri[inodekey(m)]].directory ∧ boolvar1 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ m2 = fs[ri[inodekey(m)]].size, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m5 = fs[ri[inodekey(m3)]].nsubdirs ∨ fs[ri[inodekey(m3)]].directory ∧ boolvar2 ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m5 = fs[ri[inodekey(m3)]].nsubdirs ∧ m6 = fs[ri[inodekey(m3)]].size, fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m2 = fs[ri[inodekey(m)]].size ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar1 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, fs[ri[inodekey(m3)]].directory ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m6 = fs[ri[inodekey(m3)]].size ∧ m5 = fs[ri[inodekey(m3)]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m5 = 0 ∧ ¬ boolvar2 ⊦ ⟨fail#(; ; err); asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar0) ∧ mkinode(m7, md1, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1) = old_parent_inode ∧ mkinode(m7, md1, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1) = new_parent_inode ∧ mkinode(m, md, boolvar1, m0, m1, m2) = old_child_inode ∧ mkinode(m3, md0, boolvar2, m10 + 1, m5, m6) = new_child_inode ∧ mkdentry(str, m) = old_dent ∧ mkdentry(str0, m3) = new_dent ∧ err0 = err), ⟨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}; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar0) ∧ mkinode(m7, md1, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1) = old_parent_inode ∧ mkinode(m7, md1, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1) = new_parent_inode ∧ mkinode(m, md, boolvar1, m0, m1, m2) = old_child_inode ∧ mkinode(m3, md0, boolvar2, m10 + 1, m5, m6) = new_child_inode ∧ mkdentry(str, m) = old_dent ∧ mkdentry(str0, m3) = new_dent ∧ err0 = err), m3 = 0, m3 = ROOT_INO, m7 = 0, mkdentry(str, m) = mkdentry(str0, m3), m4 = 0 ∧ m7 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1154:
¬ fs[ri[inodekey(m3)]].directory ↔ ¬ fs[ri[inodekey(m)]].directory, fs[ri[dentrykey(m7, str0)]] = dentrynode(key0, m3), fs[ri[dentrykey(m7, str)]] = dentrynode(key, m), fs[ri[inodekey(m7)]] = inodenode(key1, md2, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), m3 ≠ ROOT_INO, m3 ≠ 0, m7 ≠ 0, mkdentry(str, m) ≠ mkdentry(str0, m3), orphans(fs, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m7, str0) ∈ ri, ri[dentrykey(m7, str0)] ∈ fs, inodekey(m3) ∈ ri, inodekey(m) ∈ ri, ri[inodekey(m7)] ∈ fs, inodekey(m7) ∈ ri, ri[dentrykey(m7, str)] ∈ fs, dentrykey(m7, str) ∈ ri, ⌊err0⌋ , fs[ri[inodekey(m3)]].directory → dentrykeys(inodekey(m3), ri) = ∅, fs[ri[inodekey(m3)]].directory → abs-children(m3, fs, ri) = ∅, boolvar3 → boolvar4, m10 = 0 → links(m3, fs, ri) = ∅ ++ dentrykey(m7, str0), fs[ri[inodekey(m3)]].directory ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m6 = fs[ri[inodekey(m3)]].size ∧ m5 = fs[ri[inodekey(m3)]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m5 = 0 ∧ ¬ boolvar2, fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m2 = fs[ri[inodekey(m)]].size ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar1 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m5 = fs[ri[inodekey(m3)]].nsubdirs ∨ fs[ri[inodekey(m3)]].directory ∧ boolvar2 ∧ m10 + 1 = fs[ri[inodekey(m3)]].nlink ∧ m5 = fs[ri[inodekey(m3)]].nsubdirs ∧ m6 = fs[ri[inodekey(m3)]].size, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar1 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∨ fs[ri[inodekey(m)]].directory ∧ boolvar1 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ m2 = fs[ri[inodekey(m)]].size, links(m7, abs-dirs(fs, ri)) ≠ ∅ ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m7 = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar0) ∧ err0 = err), ⟨let old_ino = m7, new_ino = m7, boolvar0 = true in let boolvar = old_ino = new_ino ∧ mkdentry(str0, m3) = mkdentry(str, m) in {dirs := abs-dirs(fs, ri)[old_ino, abs-dirs(fs, ri)[old_ino].entries:= (abs-dirs(fs, ri)[old_ino].entries -- str)]; old_dent := mkdentry(str, m); 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[str0] := old_dent.ino; new_dent := mkdentry(str0, m3); files := abs-files(fs, ri); 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(m7, md1, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1); dirs, files); afs_inode_sync#(mkinode(m7, md1, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1); dirs, files); new_child_inode := mkinode(m3, md0, boolvar2, m10 + 1, m5, m6); 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 := (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) ); 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 := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar0) ∧ mkinode(m7, md1, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1) = old_inode ∧ mkinode(m7, md1, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1) = new_inode ∧ mkinode(m3, md0, boolvar2, m10 + 1, m5, m6) = new_child_inode ∧ mkdentry(str, m) = old_dent ∧ mkdentry(str0, m3) = new_dent ∧ err0 = err), m4 = 0 ∧ m7 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ dentrynode(key, m).ino = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%⊦ abs-file(ino, fs, ri) = mkfile (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri); (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)% ⊦ mkdentry(str, m).dentry?; (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ mkdentry(str, m).ino = m; (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (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)% ⊦ mkdentry(str, m).name = str; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ pre-rename (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) ↔ ( valid-negdentry(new_parent_inode.ino, new_dent, dirs, files) ∨ valid-dentry(new_parent_inode.ino, new_dent, dirs, files) ∧ valid-wb-inode(new_child_inode, dirs, files) ∧ new_child_inode.ino = new_dent.ino ∧ ( valid-file-ino(new_dent.ino, dirs, files) ↔ valid-file-ino(old_dent.ino, dirs, files)) ∧ ( valid-dir-ino(new_dent.ino, dirs, files) → new_dent.ino ≠ ROOT_INO ∧ dir-empty(new_dent.ino, dirs, files))) ∧ valid-dentry(old_parent_inode.ino, old_dent, dirs, files) ∧ valid-dir-inode(old_parent_inode, dirs, files) ∧ valid-dir-inode(new_parent_inode, dirs, files) ∧ ( new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta) ∧ valid-wb-inode(old_child_inode, dirs, files) ∧ old_child_inode.ino = old_dent.ino; (s)