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Proof step 188 from proof inv-rmdir (previous step)

1 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nlink, adr4 = adr1, dentrykeys(inodekey(fs[ri[dentrykey(m0, str)]].ino), ri) = ∅, links(fs[ri[dentrykey(m0, str)]].ino, fs, ri) = ∅ ++ dentrykey(m0, str), m = fs[ri[dentrykey(m0, str)]].ino, m1 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].nsubdirs, m2 = fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].size, m3 = fs[ri[inodekey(m0)]].nlink, m4 = fs[ri[inodekey(m0)]].nsubdirs, m5 = fs[ri[inodekey(m0)]].size, nd = inodenode(inodekey(m), md, true, 0, m1, m2), nd0 = dentrynode(dentrykey(m0, str), 0), nd1 = inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1), fs[ri[inodekey(m0)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m0, str)]].ino)]].directory, ro.inodes?, fo.inodes?, file-node-cons(fs, ri), log-cons(log, fs), node-cons(nd.key, nd), node-cons(nd0.key, nd0), node-cons(nd1.key, nd1), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(m0) ∈ ri, dentrykey(m0, str) ∈ ri, inodekey(fs[ri[dentrykey(m0, str)]].ino) ∈ ri, 1 ≤ fs[ri[inodekey(m0)]].size, 1 ≤ fs[ri[inodekey(m0)]].nsubdirs, m4 ≥ 1, m5 ≥ 1, ∀ adr1, adr2, adr3. ¬(new(adr1 ' + (adr2 ' + adr3), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ')), fs[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ ⟪skip⟫ (ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro)), fs[ri[dentrykey(m0, str)]].ino = ROOT_INO, fs[ri[inodekey(m0)]].nsubdirs = 0, fs[ri[inodekey(m0)]].size = 0, inodekey(m0) ∈ ro, inodekey(fs[ri[dentrykey(m0, str)]].ino) ∈ ro

Heuristic symbolic execution applied rule skip right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ dentrynode(key, m).key = key; (s)% ⊦ node-cons(key0, dentrynode(key1, ino)) ↔ key0.dentry?; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ ax + adr = ax + adr '; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ dups(adr ' + ax) ↔ adr ∈ ax ∨ dups(ax); (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)