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Proof step 9 from proof refine-link (previous step)

c_inode.ino = fs[ri[dentrykey(ino, str)]].ino, p_inode.nlink = fs[ri[inodekey(p_inode.ino)]].nlink, c_inode.nlink = fs[ri[inodekey(c_inode.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, fs[ri[inodekey(ino)]].directory, fs[ri[inodekey(p_inode.ino)]].directory, p_inode.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), dentrykey(ino, str) ∈ ri, inodekey(p_inode.ino) ∈ ri, inodekey(c_inode.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(c_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ c_inode.ino = ROOT_INO ⊦ c_inode.directory, fs[ri[inodekey(c_inode.ino)]].directory, dentrykey(p_inode.ino, str0) ∈ ri, (∃ ino0. inodekey(ino0) ∈ ri ∧ (fs[ri[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO) ∧ dentrykey(ino0, str) ∈ ri ∧ fs[ri[dentrykey(ino0, str)]].ino = c_inode.ino) ∧ (p_inode.nlink ≠ 0 ∨ p_inode.ino = ROOT_INO) ∧ (c_inode.nlink ≠ 0 ∨ c_inode.ino = ROOT_INO) ∧ 0 = fs[ri[inodekey(c_inode.ino)]].nsubdirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
p_inode.nlink = fs[ri[inodekey(p_inode.ino)]].nlink, p_inode.nsubdirs = fs[ri[inodekey(p_inode.ino)]].nsubdirs, p_inode.size = fs[ri[inodekey(p_inode.ino)]].size, ¬ boolvar0, c_inode = mkinode(m, md, boolvar0, m0, m1, m2), m = fs[ri[dentrykey(ino, str)]].ino, m0 = fs[ri[inodekey(m)]].nlink, m1 = 0, p_inode.directory, fs[ri[inodekey(p_inode.ino)]].directory, fs[ri[inodekey(ino)]].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(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, dentrykey(p_inode.ino, str0) ∈ 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) ∧ (m0 ≠ 0 ∨ m = ROOT_INO) ∧ 0 = fs[ri[inodekey(m)]].nsubdirs

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] → [c_inode, m, md, boolvar, 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: c_inode, m, md, boolvar, m0, m1, m2