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Proof step 3 from proof inv-rmdir (previous step)

fs[ri[dentrykey(p_inode.ino, dent.name)]].ino = dent.ino, c_inode.ino = dent.ino, c_inode.nlink = 1, p_inode.nlink = fs[ri[inodekey(p_inode.ino)]].nlink, p_inode.nsubdirs = fs[ri[inodekey(p_inode.ino)]].nsubdirs, c_inode.nsubdirs = fs[ri[inodekey(dent.ino)]].nsubdirs, p_inode.size = fs[ri[inodekey(p_inode.ino)]].size, c_inode.size = fs[ri[inodekey(dent.ino)]].size, 1 = fs[ri[inodekey(dent.ino)]].nlink, dentrykeys(inodekey(dent.ino), ri) = ∅, links(dent.ino, fs, ri) = ∅ ++ dentrykey(p_inode.ino, dent.name), dent.ino ≠ ROOT_INO, p_inode.nsubdirs ≠ 0, p_inode.size ≠ 0, dent.dentry?, fs[ri[inodekey(p_inode.ino)]].directory, p_inode.directory, fs[ri[inodekey(dent.ino)]].directory, c_inode.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), dentrykey(p_inode.ino, dent.name) ∈ ri, inodekey(dent.ino) ∈ ri, inodekey(p_inode.ino) ∈ ri, 1 ≤ p_inode.nsubdirs, 1 ≤ p_inode.size, ¬ inodekey(dent.ino) ∈ ro, ¬ inodekey(p_inode.ino) ∈ ro, p_inode.nlink ≠ 0 ∨ p_inode.ino = ROOT_INO ⊦ ⟪aubifs_rmdir#(fi, fo; p_inode, c_inode, dent, err, ri, ro, fs, log, boolvar)⟫ (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 4:
c_inode.ino = m, fs[ri[dentrykey(p_inode.ino, str)]].ino = m, p_inode.nlink = fs[ri[inodekey(p_inode.ino)]].nlink, c_inode.nlink = 1, c_inode.nsubdirs = fs[ri[inodekey(m)]].nsubdirs, p_inode.nsubdirs = fs[ri[inodekey(p_inode.ino)]].nsubdirs, c_inode.size = fs[ri[inodekey(m)]].size, p_inode.size = fs[ri[inodekey(p_inode.ino)]].size, 1 = fs[ri[inodekey(m)]].nlink, dent = mkdentry(str, m), dentrykeys(inodekey(m), ri) = ∅, links(m, fs, ri) = ∅ ++ dentrykey(p_inode.ino, str), dent.dentry?, c_inode.directory, fs[ri[inodekey(m)]].directory, p_inode.directory, fs[ri[inodekey(p_inode.ino)]].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), inodekey(p_inode.ino) ∈ ri, inodekey(m) ∈ ri, dentrykey(p_inode.ino, str) ∈ ri, 1 ≤ p_inode.size, 1 ≤ p_inode.nsubdirs, p_inode.nlink ≠ 0 ∨ p_inode.ino = ROOT_INO ⊦ ⟪aubifs_rmdir#(fi, fo; p_inode, c_inode, dent, err, ri, ro, fs, log, boolvar)⟫ (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)), p_inode.nsubdirs = 0, p_inode.size = 0, m = ROOT_INO, inodekey(m) ∈ ro, inodekey(p_inode.ino) ∈ ro

Rule argument

spec: dentry name: elim seq: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)) subst: [dent, str, m] → [dent, str, m]

Additional information

Used simplifier rules: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)); (elim) Used terms: dent, str, m