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Proof step 90 from proof refine-rmdir (previous step)

1 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink, abs-children(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅, c_inode = mkinode (fs[ri[dentrykey(m, str)]].ino, md0, true, 1, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size), dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), dentrykeys(inodekey(fs[ri[dentrykey(m, str)]].ino), ri) = ∅, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), ino = c_inode.ino, links(fs[ri[dentrykey(m, str)]].ino, fs, ri) = ∅ ++ dentrykey(m, str), m0 = fs[ri[inodekey(m)]].nlink, m1 = fs[ri[inodekey(m)]].nsubdirs, m2 = fs[ri[inodekey(m)]].size, m3 = fs[ri[dentrykey(m, str)]].ino, m5 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs, m6 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size, p_inode = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), ro = orphans(fs, ri), fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, fs[ri[inodekey(m)]].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)), pre-rmdir(p_inode, c_inode, dent, fs, ri, ro), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, 1 ≤ fs[ri[inodekey(m)]].nsubdirs, c_inode.nlink ≥ 1, p_inode.nsubdirs ≥ 1, p_inode.size ≥ 1, asynced → boolvar, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ [aubifs_core_journal_add3# (inodenode(inodekey(p_inode.ino), p_inode.meta, p_inode.directory, p_inode.nlink, p_inode.nsubdirs - 1, p_inode.size - 1), dentrynode(dentrykey(p_inode.ino, dent.name), 0), inodenode(inodekey(c_inode.ino), c_inode.meta, c_inode.directory, c_inode.nlink - 1, c_inode.nsubdirs, c_inode.size), ri, fi, ro, fo ; adr1, adr0, adr, fs, log ; boolvar, err); nd1 := inodenode(inodekey(p_inode.ino), p_inode.meta, p_inode.directory, p_inode.nlink, p_inode.nsubdirs - 1, p_inode.size - 1); nd := inodenode(inodekey(c_inode.ino), c_inode.meta, c_inode.directory, c_inode.nlink - 1, c_inode.nsubdirs, c_inode.size); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(p_inode.ino), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_remove#(dentrykey(p_inode.ino, dent.name), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(c_inode.ino), adr, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_orphans_insert#(inodekey(c_inode.ino), ri, fi, fo, fs, log, boolvar; ro); dent := negdentry(dent.name); p_inode := mkinode(p_inode.ino, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); c_inode := mkinode(ino, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.size)}] ( ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro) ∧ ri-inj(ri) ∧ log-cons(log, fs) ∧ ro.inodes? → ⟨old_dent := mkdentry(str, m3); p_inode0 := mkinode(m, md, true, m0, m1, m2); p_inode1 := mkinode(m3, md0, true, 1, m5, m6); afs_rmdir#(; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ err = err0)), fs[ri[dentrykey(m, str)]].ino = ROOT_INO, fs[ri[inodekey(m)]].nsubdirs = 0, fs[ri[inodekey(m)]].size = 0, fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)%⊦ valid-dir-inode(inode, fs, ri) ↔ valid-dir-ino(inode.ino, fs, ri) ∧ (inode.directory ↔ fs[ri[inodekey(inode.ino)]].directory) ∧ inode.nlink = fs[ri[inodekey(inode.ino)]].nlink ∧ inode.nsubdirs = fs[ri[inodekey(inode.ino)]].nsubdirs ∧ inode.size = fs[ri[inodekey(inode.ino)]].size; (s)% ⊦ {key} = ∅ ++ key; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ valid-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ key ∈ orphans(fs, ri) ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO; (s)%⊦ valid-dir-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-parent-ino(ino, fs, ri, ro) ↔ ( valid-dir-ino(ino, fs, ri) ∧ (fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO)) ∧ ¬ inodekey(ino) ∈ ro; (s)% ⊦ mkdentry(str, m).dentry?; (s)%⊦ valid-dentry(ino, dent, fs, ri, ro) ↔ dent.dentry? ∧ valid-parent-ino(ino, fs, ri, ro) ∧ valid-ino(dent.ino, fs, ri) ∧ dentrykey(ino, dent.name) ∈ ri ∧ fs[ri[dentrykey(ino, dent.name)]].ino = dent.ino; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ mkdentry(str, m).ino = m; (s)%⊦ pre-rmdir(p_inode, c_inode, dent, fs, ri, ro) ↔ dent.ino ≠ ROOT_INO ∧ valid-dentry(p_inode.ino, dent, fs, ri, ro) ∧ fs[ri[inodekey(dent.ino)]].nlink = 1 ∧ links(dent.ino, fs, ri) = {dentrykey(p_inode.ino, dent.name)} ∧ dentrykeys(inodekey(dent.ino), ri) = ∅ ∧ ¬ inodekey(dent.ino) ∈ ro ∧ valid-dir-inode(p_inode, fs, ri) ∧ valid-dir-inode(c_inode, fs, ri) ∧ c_inode.ino = dent.ino ∧ p_inode.nsubdirs ≥ 1 ∧ p_inode.size ≥ 1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)