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Proof step 374 from proof inv-unlink (previous step)

c_inode.ino = fs[ri[dentrykey(p_inode.ino, str)]].ino, c_inode.nlink = fs[ri[inodekey(c_inode.ino)]].nlink, p_inode.nlink = fs[ri[inodekey(p_inode.ino)]].nlink, c_inode.nsubdirs = fs[ri[inodekey(c_inode.ino)]].nsubdirs, p_inode.nsubdirs = fs[ri[inodekey(p_inode.ino)]].nsubdirs, p_inode.size = fs[ri[inodekey(p_inode.ino)]].size, dent = mkdentry(str, c_inode.ino), 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(c_inode.ino) ∈ ri, dentrykey(p_inode.ino, str) ∈ ri, 1 ≤ p_inode.size, c_inode.nlink = 1 → links(c_inode.ino, fs, ri) = ∅ ++ dentrykey(p_inode.ino, str), p_inode.nlink ≠ 0 ∨ p_inode.ino = ROOT_INO ⊦ c_inode.ino = ROOT_INO, c_inode.nlink = 0, p_inode.size = 0, fs[ri[inodekey(c_inode.ino)]].directory, c_inode.directory, pre-unlink(p_inode, c_inode, dent, fs, ri, ro), inodekey(p_inode.ino) ∈ ro, inodekey(c_inode.ino) ∈ ro

Heuristic simplifier applied rule simplifier

And closed the goal!

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)%⊦ 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)%⊦ 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)% ⊦ 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)