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Proof step 5 from proof refine-link (previous step)

old_dent.ino = fs[ri[dentrykey(ino, old_dent.name)]].ino, c_inode.ino = old_dent.ino, p_inode.nlink = fs[ri[inodekey(p_inode.ino)]].nlink, c_inode.nlink = fs[ri[inodekey(old_dent.ino)]].nlink, p_inode.nsubdirs = fs[ri[inodekey(p_inode.ino)]].nsubdirs, c_inode.nsubdirs = 0, p_inode.size = fs[ri[inodekey(p_inode.ino)]].size, old_dent.dentry?, fs[ri[inodekey(ino)]].directory, fs[ri[inodekey(p_inode.ino)]].directory, p_inode.directory, fo.inodes?, orphans(fs, ri).inodes?, new_dent.negdentry?, 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), dentrykey(ino, old_dent.name) ∈ ri, inodekey(p_inode.ino) ∈ ri, inodekey(old_dent.ino) ∈ ri, inodekey(ino) ∈ ri, asynced → boolvar, links(ino, abs-dirs(fs, ri)) ≠ ∅ ∨ ino = ROOT_INO, links(p_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ p_inode.ino = ROOT_INO, links(old_dent.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ old_dent.ino = ROOT_INO ⊦ c_inode.directory, fs[ri[inodekey(old_dent.ino)]].directory, dentrykey(p_inode.ino, new_dent.name) ∈ ri, (∃ ino0. inodekey(ino0) ∈ ri ∧ (fs[ri[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO) ∧ dentrykey(ino0, old_dent.name) ∈ ri ∧ fs[ri[dentrykey(ino0, old_dent.name)]].ino = old_dent.ino) ∧ (p_inode.nlink ≠ 0 ∨ p_inode.ino = ROOT_INO) ∧ (c_inode.nlink ≠ 0 ∨ old_dent.ino = ROOT_INO) ∧ 0 = fs[ri[inodekey(old_dent.ino)]].nsubdirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
c_inode.ino = m, c_inode.nlink = fs[ri[inodekey(m)]].nlink, p_inode.nlink = fs[ri[inodekey(p_inode.ino)]].nlink, c_inode.nsubdirs = 0, p_inode.nsubdirs = fs[ri[inodekey(p_inode.ino)]].nsubdirs, p_inode.size = fs[ri[inodekey(p_inode.ino)]].size, m = fs[ri[dentrykey(ino, str)]].ino, old_dent = mkdentry(str, m), old_dent.dentry?, p_inode.directory, fs[ri[inodekey(p_inode.ino)]].directory, fs[ri[inodekey(ino)]].directory, orphans(fs, ri).inodes?, fo.inodes?, new_dent.negdentry?, 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(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(ino) ∈ ri, inodekey(m) ∈ ri, inodekey(p_inode.ino) ∈ ri, dentrykey(ino, str) ∈ ri, asynced → boolvar, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, links(p_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ p_inode.ino = ROOT_INO, links(ino, abs-dirs(fs, ri)) ≠ ∅ ∨ ino = ROOT_INO ⊦ fs[ri[inodekey(m)]].directory, c_inode.directory, dentrykey(p_inode.ino, new_dent.name) ∈ ri, (∃ ino0. inodekey(ino0) ∈ ri ∧ (fs[ri[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO) ∧ dentrykey(ino0, str) ∈ ri ∧ fs[ri[dentrykey(ino0, str)]].ino = m) ∧ (p_inode.nlink ≠ 0 ∨ p_inode.ino = ROOT_INO) ∧ (c_inode.nlink ≠ 0 ∨ m = ROOT_INO) ∧ 0 = fs[ri[inodekey(m)]].nsubdirs

Rule argument

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

Additional information

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