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Proof step 11 from proof inv-rename-overwrite-keep-parent (previous step)

fs[ri[dentrykey(m, str0)]].ino = new_child_inode.ino, ¬ fs[ri[inodekey(new_child_inode.ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, new_dent = mkdentry(str0, new_child_inode.ino), old_dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), parent_inode = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), new_child_inode.ino ≠ ROOT_INO, new_child_inode.nlink ≠ 0, fs[ri[inodekey(m)]].size ≠ 0, fs[ri[inodekey(m)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), dentrykey(m, str) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str0) ∈ ri, inodekey(new_child_inode.ino) ∈ ri, inodekey(m) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, ¬ inodekey(m) ∈ ro, boolvar → 1 ≤ fs[ri[inodekey(m)]].nsubdirs, new_child_inode.nlink = 1 → links(new_child_inode.ino, fs, ri) = ∅ ++ dentrykey(m, str0), fs[ri[inodekey(new_child_inode.ino)]].directory → dentrykeys(inodekey(new_child_inode.ino), ri) = ∅, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, ¬ fs[ri[inodekey(new_child_inode.ino)]].directory ∧ ¬ boolvar ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ boolvar ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size, ¬ fs[ri[inodekey(new_child_inode.ino)]].directory ∧ ¬ new_child_inode.directory ∧ new_child_inode.nlink = fs[ri[inodekey(new_child_inode.ino)]].nlink ∧ new_child_inode.nsubdirs = fs[ri[inodekey(new_child_inode.ino)]].nsubdirs ∨ fs[ri[inodekey(new_child_inode.ino)]].directory ∧ new_child_inode.directory ∧ new_child_inode.nlink = fs[ri[inodekey(new_child_inode.ino)]].nlink ∧ new_child_inode.nsubdirs = fs[ri[inodekey(new_child_inode.ino)]].nsubdirs ∧ new_child_inode.size = fs[ri[inodekey(new_child_inode.ino)]].size ⊦ ⟪aubifs_rename_overwrite_keep_parent# (boolvar, mkinode(fs[ri[dentrykey(m, str)]].ino, md0, boolvar, m1, m2, m3), fi, fo ; parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0)⟫ (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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
fs[ri[dentrykey(m, str0)]].ino = m0, ¬ fs[ri[inodekey(m0)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, new_child_inode = mkinode(m0, md1, boolvar1, m4, m5, m6), new_dent = mkdentry(str0, m0), old_dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), parent_inode = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), fs[ri[inodekey(m)]].directory, ro.inodes?, fo.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(m) ∈ ri, inodekey(m0) ∈ ri, dentrykey(m, str0) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, fs[ri[inodekey(m0)]].directory → dentrykeys(inodekey(m0), ri) = ∅, m4 = 1 → links(m0, fs, ri) = ∅ ++ dentrykey(m, str0), boolvar → 1 ≤ fs[ri[inodekey(m)]].nsubdirs, ¬ fs[ri[inodekey(m0)]].directory ∧ ¬ boolvar1 ∧ m4 = fs[ri[inodekey(m0)]].nlink ∧ m5 = fs[ri[inodekey(m0)]].nsubdirs ∨ fs[ri[inodekey(m0)]].directory ∧ boolvar1 ∧ m4 = fs[ri[inodekey(m0)]].nlink ∧ m5 = fs[ri[inodekey(m0)]].nsubdirs ∧ m6 = fs[ri[inodekey(m0)]].size, ¬ fs[ri[inodekey(m0)]].directory ∧ ¬ boolvar ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ boolvar ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟪aubifs_rename_overwrite_keep_parent# (boolvar, mkinode(fs[ri[dentrykey(m, str)]].ino, md0, boolvar, m1, m2, m3), fi, fo ; parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0)⟫ (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)), fs[ri[inodekey(m)]].size = 0, m0 = ROOT_INO, m4 = 0, inodekey(m) ∈ ro

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [new_child_inode, m0, md1, boolvar1, m4, m5, m6]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: new_child_inode, m0, md1, boolvar1, m4, m5, m6