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Proof step 7 from proof refine-rmdir (previous step)

c_inode.ino = fs[ri[dentrykey(p_inode.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 = fs[ri[inodekey(c_inode.ino)]].nsubdirs, p_inode.size = fs[ri[inodekey(p_inode.ino)]].size, c_inode.size = fs[ri[inodekey(c_inode.ino)]].size, abs-children(c_inode.ino, fs, ri) = ∅, fs[ri[inodekey(p_inode.ino)]].directory, p_inode.directory, fs[ri[inodekey(c_inode.ino)]].directory, c_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(p_inode.ino, str) ∈ ri, inodekey(c_inode.ino) ∈ ri, inodekey(p_inode.ino) ∈ ri, asynced → boolvar, links(p_inode.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ p_inode.ino = ROOT_INO ⊦ c_inode.ino = ROOT_INO, (p_inode.nlink ≠ 0 ∨ p_inode.ino = ROOT_INO) ∧ c_inode.nlink = 1 ∧ links(c_inode.ino, fs, ri) = ∅ ++ dentrykey(p_inode.ino, str) ∧ dentrykeys(inodekey(c_inode.ino), ri) = ∅ ∧ c_inode.nlink ≠ 0 ∧ 1 ≤ p_inode.nsubdirs ∧ 1 ≤ p_inode.size

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
c_inode.ino = fs[ri[dentrykey(m, str)]].ino, c_inode.nlink = fs[ri[inodekey(c_inode.ino)]].nlink, c_inode.nsubdirs = fs[ri[inodekey(c_inode.ino)]].nsubdirs, c_inode.size = fs[ri[inodekey(c_inode.ino)]].size, abs-children(c_inode.ino, fs, ri) = ∅, boolvar0, m0 = fs[ri[inodekey(m)]].nlink, m1 = fs[ri[inodekey(m)]].nsubdirs, m2 = fs[ri[inodekey(m)]].size, p_inode = mkinode(m, md, boolvar0, m0, m1, m2), c_inode.directory, fs[ri[inodekey(c_inode.ino)]].directory, fs[ri[inodekey(m)]].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(m) ∈ ri, inodekey(c_inode.ino) ∈ ri, dentrykey(m, str) ∈ ri, asynced → boolvar, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ c_inode.ino = ROOT_INO, (m0 ≠ 0 ∨ m = ROOT_INO) ∧ c_inode.nlink = 1 ∧ links(c_inode.ino, fs, ri) = ∅ ++ dentrykey(m, str) ∧ dentrykeys(inodekey(c_inode.ino), ri) = ∅ ∧ c_inode.nlink ≠ 0 ∧ 1 ≤ m1 ∧ 1 ≤ m2

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_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: p_inode, m, md, boolvar, m0, m1, m2