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Proof step 11 from proof refine-unlink (previous step)

c_inode = mkinode(fs[ri[dentrykey(m, str)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink, 0, m6), dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), 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, m4 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink, 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(m)]].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-inj(fi), ri-inj(ri), 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, asynced → boolvar, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, 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) ∧ ri-inj(fi) ∧ log-cons(log, fs) ∧ ro.inodes? ∧ fo.inodes? ∧ pre-unlink(p_inode, c_inode, dent, fs, ri, ro)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

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