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Proof step 11 from proof rename-precond-abs (previous step)

old_child_inode.ino = fs[ri[dentrykey(m4, str)]].ino, fs[ri[inodekey(m4)]].directory, fs[ri[inodekey(m3)]].directory, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), 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(m4, str) ∈ ri, inodekey(m3) ∈ ri, inodekey(m4) ∈ ri, m3 = m4 → md = md0, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO, inodekey(old_child_inode.ino) ∈ ri ∧ fs[ri[inodekey(old_child_inode.ino)]].directory ∨ inodekey(old_child_inode.ino) ∈ ri ∧ ¬ fs[ri[inodekey(old_child_inode.ino)]].directory, inodekey(old_child_inode.ino) ∈ ri ∧ fs[ri[inodekey(old_child_inode.ino)]].directory ∧ old_child_inode.nlink = fs[ri[inodekey(old_child_inode.ino)]].nlink ∧ old_child_inode.size = fs[ri[inodekey(old_child_inode.ino)]].size ∧ old_child_inode.nsubdirs = fs[ri[inodekey(old_child_inode.ino)]].nsubdirs ∧ old_child_inode.directory ∨ inodekey(old_child_inode.ino) ∈ ri ∧ ¬ fs[ri[inodekey(old_child_inode.ino)]].directory ∧ old_child_inode.nlink = fs[ri[inodekey(old_child_inode.ino)]].nlink ∧ old_child_inode.nsubdirs = 0 ∧ ¬ old_child_inode.directory, (links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO) ∧ ¬ dentrykey(m3, new_dent.name) ∈ ri ∧ new_dent.negdentry? ∨ (links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO) ∧ (inodekey(new_dent.ino) ∈ ri ∧ fs[ri[inodekey(new_dent.ino)]].directory ∨ inodekey(new_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_dent.ino)]].directory) ∧ dentrykey(m3, new_dent.name) ∈ ri ∧ new_dent.ino = fs[ri[dentrykey(m3, new_dent.name)]].ino ∧ new_dent.dentry? ∧ ( inodekey(new_dent.ino) ∈ ri ∧ fs[ri[inodekey(new_dent.ino)]].directory ∧ m0 = fs[ri[inodekey(new_dent.ino)]].nlink ∧ m2 = fs[ri[inodekey(new_dent.ino)]].size ∧ m1 = fs[ri[inodekey(new_dent.ino)]].nsubdirs ∧ boolvar ∨ inodekey(new_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_dent.ino)]].directory ∧ m0 = fs[ri[inodekey(new_dent.ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar) ∧ m = new_dent.ino ∧ ( inodekey(new_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_dent.ino)]].directory ↔ inodekey(old_child_inode.ino) ∈ ri ∧ ¬ fs[ri[inodekey(old_child_inode.ino)]].directory) ∧ (inodekey(new_dent.ino) ∈ ri ∧ fs[ri[inodekey(new_dent.ino)]].directory → new_dent.ino ≠ ROOT_INO ∧ abs-children(new_dent.ino, fs, ri) = ∅) ⊦ ( new_dent.negdentry? ∧ (fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO) ∧ ¬ dentrykey(m3, new_dent.name) ∈ ri ∨ new_dent.dentry? ∧ (fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO) ∧ inodekey(new_dent.ino) ∈ ri ∧ dentrykey(m3, new_dent.name) ∈ ri ∧ fs[ri[dentrykey(m3, new_dent.name)]].ino = new_dent.ino ∧ ( ¬ fs[ri[inodekey(new_dent.ino)]].directory ∧ ¬ boolvar ∧ m0 = fs[ri[inodekey(new_dent.ino)]].nlink ∧ m1 = fs[ri[inodekey(new_dent.ino)]].nsubdirs ∨ fs[ri[inodekey(new_dent.ino)]].directory ∧ boolvar ∧ m0 = fs[ri[inodekey(new_dent.ino)]].nlink ∧ m1 = fs[ri[inodekey(new_dent.ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(new_dent.ino)]].size) ∧ m = new_dent.ino ∧ (¬ fs[ri[inodekey(new_dent.ino)]].directory ↔ ¬ fs[ri[inodekey(old_child_inode.ino)]].directory) ∧ (fs[ri[inodekey(new_dent.ino)]].directory → dentrykeys(inodekey(new_dent.ino), ri) = ∅) ∧ new_dent.ino ≠ ROOT_INO ∧ m0 ≠ 0 ∧ (m0 = 1 → links(new_dent.ino, fs, ri) = ∅ ++ dentrykey(m3, new_dent.name))) ∧ (fs[ri[inodekey(m4)]].nlink ≠ 0 ∨ m4 = ROOT_INO) ∧ inodekey(old_child_inode.ino) ∈ ri ∧ ( ¬ fs[ri[inodekey(old_child_inode.ino)]].directory ∧ ¬ old_child_inode.directory ∧ old_child_inode.nlink = fs[ri[inodekey(old_child_inode.ino)]].nlink ∧ old_child_inode.nsubdirs = fs[ri[inodekey(old_child_inode.ino)]].nsubdirs ∨ fs[ri[inodekey(old_child_inode.ino)]].directory ∧ old_child_inode.directory ∧ old_child_inode.nlink = fs[ri[inodekey(old_child_inode.ino)]].nlink ∧ old_child_inode.nsubdirs = fs[ri[inodekey(old_child_inode.ino)]].nsubdirs ∧ old_child_inode.size = fs[ri[inodekey(old_child_inode.ino)]].size) ∧ 1 ≤ fs[ri[inodekey(m4)]].size ∧ (old_child_inode.directory → 1 ≤ fs[ri[inodekey(m4)]].nsubdirs)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
m5 = fs[ri[dentrykey(m4, str)]].ino, old_child_inode = mkinode(m5, md1, boolvar0, m6, m7, m8), fs[ri[inodekey(m3)]].directory, fs[ri[inodekey(m4)]].directory, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), 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(m4) ∈ ri, inodekey(m3) ∈ ri, dentrykey(m4, str) ∈ ri, m3 = m4 → md = md0, (links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO) ∧ ¬ dentrykey(m3, new_dent.name) ∈ ri ∧ new_dent.negdentry? ∨ (links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO) ∧ (inodekey(new_dent.ino) ∈ ri ∧ fs[ri[inodekey(new_dent.ino)]].directory ∨ inodekey(new_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_dent.ino)]].directory) ∧ dentrykey(m3, new_dent.name) ∈ ri ∧ new_dent.ino = fs[ri[dentrykey(m3, new_dent.name)]].ino ∧ new_dent.dentry? ∧ ( inodekey(new_dent.ino) ∈ ri ∧ fs[ri[inodekey(new_dent.ino)]].directory ∧ m0 = fs[ri[inodekey(new_dent.ino)]].nlink ∧ m2 = fs[ri[inodekey(new_dent.ino)]].size ∧ m1 = fs[ri[inodekey(new_dent.ino)]].nsubdirs ∧ boolvar ∨ inodekey(new_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_dent.ino)]].directory ∧ m0 = fs[ri[inodekey(new_dent.ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar) ∧ m = new_dent.ino ∧ (inodekey(new_dent.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_dent.ino)]].directory ↔ inodekey(m5) ∈ ri ∧ ¬ fs[ri[inodekey(m5)]].directory) ∧ (inodekey(new_dent.ino) ∈ ri ∧ fs[ri[inodekey(new_dent.ino)]].directory → new_dent.ino ≠ ROOT_INO ∧ abs-children(new_dent.ino, fs, ri) = ∅), inodekey(m5) ∈ ri ∧ fs[ri[inodekey(m5)]].directory ∧ m6 = fs[ri[inodekey(m5)]].nlink ∧ m8 = fs[ri[inodekey(m5)]].size ∧ m7 = fs[ri[inodekey(m5)]].nsubdirs ∧ boolvar0 ∨ inodekey(m5) ∈ ri ∧ ¬ fs[ri[inodekey(m5)]].directory ∧ m6 = fs[ri[inodekey(m5)]].nlink ∧ m7 = 0 ∧ ¬ boolvar0, inodekey(m5) ∈ ri ∧ fs[ri[inodekey(m5)]].directory ∨ inodekey(m5) ∈ ri ∧ ¬ fs[ri[inodekey(m5)]].directory, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO ⊦ ( new_dent.negdentry? ∧ (fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO) ∧ ¬ dentrykey(m3, new_dent.name) ∈ ri ∨ new_dent.dentry? ∧ (fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO) ∧ inodekey(new_dent.ino) ∈ ri ∧ dentrykey(m3, new_dent.name) ∈ ri ∧ fs[ri[dentrykey(m3, new_dent.name)]].ino = new_dent.ino ∧ ( ¬ fs[ri[inodekey(new_dent.ino)]].directory ∧ ¬ boolvar ∧ m0 = fs[ri[inodekey(new_dent.ino)]].nlink ∧ m1 = fs[ri[inodekey(new_dent.ino)]].nsubdirs ∨ fs[ri[inodekey(new_dent.ino)]].directory ∧ boolvar ∧ m0 = fs[ri[inodekey(new_dent.ino)]].nlink ∧ m1 = fs[ri[inodekey(new_dent.ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(new_dent.ino)]].size) ∧ m = new_dent.ino ∧ (¬ fs[ri[inodekey(new_dent.ino)]].directory ↔ ¬ fs[ri[inodekey(m5)]].directory) ∧ (fs[ri[inodekey(new_dent.ino)]].directory → dentrykeys(inodekey(new_dent.ino), ri) = ∅) ∧ new_dent.ino ≠ ROOT_INO ∧ m0 ≠ 0 ∧ (m0 = 1 → links(new_dent.ino, fs, ri) = ∅ ++ dentrykey(m3, new_dent.name))) ∧ (fs[ri[inodekey(m4)]].nlink ≠ 0 ∨ m4 = ROOT_INO) ∧ inodekey(m5) ∈ ri ∧ ( ¬ fs[ri[inodekey(m5)]].directory ∧ ¬ boolvar0 ∧ m6 = fs[ri[inodekey(m5)]].nlink ∧ m7 = fs[ri[inodekey(m5)]].nsubdirs ∨ fs[ri[inodekey(m5)]].directory ∧ boolvar0 ∧ m6 = fs[ri[inodekey(m5)]].nlink ∧ m7 = fs[ri[inodekey(m5)]].nsubdirs ∧ m8 = fs[ri[inodekey(m5)]].size) ∧ 1 ≤ fs[ri[inodekey(m4)]].size ∧ (boolvar0 → 1 ≤ fs[ri[inodekey(m4)]].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] → [old_child_inode, m5, md, boolvar0, m6, m7, m8]

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: old_child_inode, m5, md, boolvar0, m6, m7, m8