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

p_inode1.ino = fs[ri[dentrykey(p_inode0.ino, str)]].ino, p_inode1.nlink = fs[ri[inodekey(p_inode1.ino)]].nlink, p_inode0.nlink = fs[ri[inodekey(p_inode0.ino)]].nlink, p_inode1.nsubdirs = 0, p_inode0.nsubdirs = fs[ri[inodekey(p_inode0.ino)]].nsubdirs, p_inode0.size = fs[ri[inodekey(p_inode0.ino)]].size, c_inode = p_inode1, dent = mkdentry(str, p_inode1.ino), dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), p_inode = p_inode0, ro = orphans(fs, ri), fs[ri[inodekey(p_inode0.ino)]].directory, p_inode0.directory, orphans(fs, ri).inodes?, fo.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(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(p_inode0.ino) ∈ ri, dentrykey(p_inode0.ino, str) ∈ ri, inodekey(p_inode1.ino) ∈ ri, ¬ fs[ri[inodekey(p_inode1.ino)]].directory, ¬ p_inode1.directory, asynced → boolvar, links(p_inode0.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ p_inode0.ino = ROOT_INO ⊦ ⟪aubifs_unlink#(fi, fo; p_inode, c_inode, dent, err, ri, ro, fs, log, boolvar)⟫ ⟨old_dent := mkdentry(str, p_inode1.ino); afs_unlink#(; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
p_inode1.ino = fs[ri[dentrykey(m, str)]].ino, p_inode1.nlink = fs[ri[inodekey(p_inode1.ino)]].nlink, p_inode1.nsubdirs = 0, boolvar0, c_inode = p_inode1, dent = mkdentry(str, p_inode1.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, p_inode = p_inode0, p_inode0 = mkinode(m, md, boolvar0, m0, m1, m2), 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(p_inode1.ino) ∈ ri, dentrykey(m, str) ∈ ri, inodekey(m) ∈ ri, asynced → boolvar, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪aubifs_unlink#(fi, fo; p_inode, c_inode, dent, err, ri, ro, fs, log, boolvar)⟫ ⟨old_dent := mkdentry(str, p_inode1.ino); afs_unlink#(; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ err = err0), fs[ri[inodekey(p_inode1.ino)]].directory, p_inode1.directory

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] → [p_inode0, m, md, boolvar0, m0, m1, m2]

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: p_inode0, m, md, boolvar0, m0, m1, m2