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Proof step 458 from proof refine-rename-overwrite-keep-parent-identity (previous step)

dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), new_dent_inode = mkinode(fs[ri[dentrykey(m6, str)]].ino, md, boolvar3, m0, m1, m2), new_inode = mkinode(m6, md1, true, fs[ri[inodekey(m6)]].nlink, fs[ri[inodekey(m6)]].nsubdirs, fs[ri[inodekey(m6)]].size), old_dent1 = mkdentry(str, fs[ri[dentrykey(m6, str)]].ino), old_dent2 = mkdentry(str, fs[ri[dentrykey(m6, str)]].ino), old_dent_inode = mkinode(fs[ri[dentrykey(m6, str)]].ino, md0, boolvar2, m3, m4, m5), old_inode = mkinode(m6, md1, true, fs[ri[inodekey(m6)]].nlink, fs[ri[inodekey(m6)]].nsubdirs, fs[ri[inodekey(m6)]].size), fs[ri[dentrykey(m6, str)]].ino ≠ ROOT_INO, fs[ri[dentrykey(m6, str)]].ino ≠ 0, fs[ri[inodekey(m6)]].size ≠ 0, m0 ≠ 0, m6 ≠ 0, fs[ri[inodekey(m6)]].directory, 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)), 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), inodekey(m6) ∈ ri, inodekey(fs[ri[dentrykey(m6, str)]].ino) ∈ ri, dentrykey(m6, str) ∈ ri, 1 ≤ fs[ri[inodekey(m6)]].size, boolvar2 → 1 ≤ fs[ri[inodekey(m6)]].nsubdirs, m0 = 1 → links(fs[ri[dentrykey(m6, str)]].ino, fs, ri) = ∅ ++ dentrykey(m6, str), boolvar4 → boolvar1, fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory → abs-children(fs[ri[dentrykey(m6, str)]].ino, fs, ri) = ∅, fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(m6, str)]].ino), ri) = ∅, ∀ adr, adr0, adr1, adr2. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr2 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr = adr2 ∨ adr0 = adr1 ∨ adr0 = adr2 ∨ adr1 = adr2, fs[ri[inodekey(m6)]].nlink ≠ 0 ∨ m6 = ROOT_INO, links(m6, abs-dirs(fs, ri)) ≠ ∅ ∨ m6 = ROOT_INO, ¬ fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ ¬ boolvar2 ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ boolvar2 ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nsubdirs ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ ¬ boolvar3 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ boolvar3 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].size, fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].size ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m4 = 0 ∧ ¬ boolvar2, fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].size ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nsubdirs ∧ boolvar3 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar3 ⊦ ⟨afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent1, old_dent2, err0, dirs, files; boolvar4)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (boolvar4 → boolvar0) ∧ mkinode(m6, md1, true, fs[ri[inodekey(m6)]].nlink, fs[ri[inodekey(m6)]].nsubdirs, fs[ri[inodekey(m6)]].size) = old_inode ∧ mkinode(m6, md1, true, fs[ri[inodekey(m6)]].nlink, fs[ri[inodekey(m6)]].nsubdirs, fs[ri[inodekey(m6)]].size) = new_inode ∧ mkinode(fs[ri[dentrykey(m6, str)]].ino, md0, boolvar2, m3, m4, m5) = old_dent_inode ∧ mkinode(fs[ri[dentrykey(m6, str)]].ino, md, boolvar3, m0, m1, m2) = new_dent_inode ∧ mkdentry(str, fs[ri[dentrykey(m6, str)]].ino) = old_dent1 ∧ mkdentry(str, fs[ri[dentrykey(m6, str)]].ino) = old_dent2 ∧ ENOSPC = err0), fs[ri[inodekey(m6)]].nlink = 0 ∧ m6 ≠ ROOT_INO

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 459:
dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), new_child_inode = new_dent_inode, new_dent = old_dent2, new_dent_inode = mkinode(fs[ri[dentrykey(m6, str)]].ino, md, boolvar3, m0, m1, m2), new_inode = mkinode(m6, md1, true, fs[ri[inodekey(m6)]].nlink, fs[ri[inodekey(m6)]].nsubdirs, fs[ri[inodekey(m6)]].size), new_parent_inode = new_inode, old_child_inode = old_dent_inode, old_dent = old_dent1, old_dent1 = mkdentry(str, fs[ri[dentrykey(m6, str)]].ino), old_dent2 = mkdentry(str, fs[ri[dentrykey(m6, str)]].ino), old_dent_inode = mkinode(fs[ri[dentrykey(m6, str)]].ino, md0, boolvar2, m3, m4, m5), old_inode = mkinode(m6, md1, true, fs[ri[inodekey(m6)]].nlink, fs[ri[inodekey(m6)]].nsubdirs, fs[ri[inodekey(m6)]].size), old_parent_inode = old_inode, fs[ri[inodekey(m6)]].directory, 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(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m6, str) ∈ ri, inodekey(fs[ri[dentrykey(m6, str)]].ino) ∈ ri, inodekey(m6) ∈ ri, 1 ≤ fs[ri[inodekey(m6)]].size, fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(m6, str)]].ino), ri) = ∅, fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory → abs-children(fs[ri[dentrykey(m6, str)]].ino, fs, ri) = ∅, boolvar4 → boolvar1, m0 = 1 → links(fs[ri[dentrykey(m6, str)]].ino, fs, ri) = ∅ ++ dentrykey(m6, str), boolvar2 → 1 ≤ fs[ri[inodekey(m6)]].nsubdirs, ∀ adr, adr0, adr1, adr2. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr2 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr = adr2 ∨ adr0 = adr1 ∨ adr0 = adr2 ∨ adr1 = adr2, fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].size ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nsubdirs ∧ boolvar3 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar3, fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].size ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m4 = 0 ∧ ¬ boolvar2, ¬ fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ ¬ boolvar3 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ boolvar3 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ ¬ boolvar2 ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].directory ∧ boolvar2 ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nlink ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].nsubdirs ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m6, str)]].ino)]].size, links(m6, abs-dirs(fs, ri)) ≠ ∅ ∨ m6 = ROOT_INO, fs[ri[inodekey(m6)]].nlink ≠ 0 ∨ m6 = ROOT_INO ⊦ ⟨if pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) then { 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 := ?} else abort⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar0) ∧ mkinode(m6, md1, true, fs[ri[inodekey(m6)]].nlink, fs[ri[inodekey(m6)]].nsubdirs, fs[ri[inodekey(m6)]].size) = old_parent_inode ∧ mkinode(m6, md1, true, fs[ri[inodekey(m6)]].nlink, fs[ri[inodekey(m6)]].nsubdirs, fs[ri[inodekey(m6)]].size) = new_parent_inode ∧ mkinode(fs[ri[dentrykey(m6, str)]].ino, md0, boolvar2, m3, m4, m5) = old_child_inode ∧ mkinode(fs[ri[dentrykey(m6, str)]].ino, md, boolvar3, m0, m1, m2) = new_child_inode ∧ mkdentry(str, fs[ri[dentrykey(m6, str)]].ino) = old_dent ∧ mkdentry(str, fs[ri[dentrykey(m6, str)]].ino) = new_dent ∧ ENOSPC = err), fs[ri[dentrykey(m6, str)]].ino = ROOT_INO, fs[ri[dentrykey(m6, str)]].ino = 0, fs[ri[inodekey(m6)]].size = 0, m0 = 0, m6 = 0, fs[ri[inodekey(m6)]].nlink = 0 ∧ m6 ≠ ROOT_INO

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_rename# (; OLD_PARENT_INODE, NEW_PARENT_INODE, OLD_CHILD_INODE, NEW_CHILD_INODE, OLD_DENT, NEW_DENT, ERR, DIRS, FILES ; ASYNCED ) {if pre-rename (OLD_PARENT_INODE, OLD_DENT, OLD_CHILD_INODE, NEW_PARENT_INODE, NEW_DENT, NEW_CHILD_INODE, DIRS, FILES) then { let OLD_INO = OLD_PARENT_INODE.ino, NEW_INO = NEW_PARENT_INODE.ino, OVERWRITE = NEW_DENT.dentry? in let IDENTITY = OLD_INO = NEW_INO ∧ NEW_DENT = OLD_DENT in {DIRS[OLD_INO].entries := DIRS[OLD_INO].entries -- OLD_DENT.name; if ¬ IDENTITY 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 OVERWRITE ∧ ¬ IDENTITY then let INO = NEW_DENT.ino in afs_drop_nlink#(INO; DIRS, FILES); if ¬ OVERWRITE 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 OVERWRITE 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 := ?} else abort };