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Proof step 471 from proof refine-rmdir (previous step)

1 = fs[ri[inodekey(m0)]].nlink, fs[ri[dentrykey(m, str)]] = dentrynode(key, m0), fs[ri[inodekey(m)]] = inodenode(key0, md1, true, m1, m2, m3), abs-children(m0, fs, ri) = ∅, dentrykeys(inodekey(m0), ri) = ∅, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), links(m0, fs, ri) = ∅ ++ dentrykey(m, str), old_dent = mkdentry(str, m0), p_inode0 = mkinode(m, md, true, m1, m2, m3), p_inode1 = mkinode(m0, md0, true, 1, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size), m ≠ 0, m0 ≠ ROOT_INO, m0 ≠ 0, m2 ≠ 0, m3 ≠ 0, fs[ri[inodekey(m0)]].directory, fs[ri[inodekey(m0)]].inode?, 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-cons(ri, fs), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m, str) ∈ ri, ri[dentrykey(m, str)] ∈ fs, ri[inodekey(m0)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, 1 ≤ m3, 1 ≤ m2, ⌊err0⌋ , asynced → boolvar0, m1 ≠ 0 ∨ m = ROOT_INO, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_rmdir#(; p_inode0, p_inode1, old_dent, err1, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m1, m2, m3) = p_inode0 ∧ mkinode(m0, md0, true, 1, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size) = p_inode1 ∧ mkdentry(str, m0) = old_dent ∧ err0 = err1), m1 = 0 ∧ m ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 472:
1 = m4, fs[ri[inodekey(m)]] = inodenode(key0, md1, true, m1, m2, m3), fs[ri[dentrykey(m, str)]] = dentrynode(key, m0), fs[ri[inodekey(m0)]] = inodenode(key1, md2, boolvar1, m4, m5, m6), abs-children(m0, fs, ri) = ∅, boolvar1, dentrykeys(inodekey(m0), ri) = ∅, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), links(m0, fs, ri) = ∅ ++ dentrykey(m, str), old_dent = mkdentry(str, m0), p_inode0 = mkinode(m, md, true, m1, m2, m3), p_inode1 = mkinode(m0, md0, true, 1, m5, m6), fs[ri[inodekey(m0)]].inode?, 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-cons(ri, fs), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m0)] ∈ fs, ri[dentrykey(m, str)] ∈ fs, dentrykey(m, str) ∈ ri, 1 ≤ m2, 1 ≤ m3, ⌊err0⌋ , asynced → boolvar0, links(m, abs-dirs(fs, ri)) ≠ ∅ ∨ m = ROOT_INO, m1 ≠ 0 ∨ m = ROOT_INO ⊦ ⟨afs_rmdir#(; p_inode0, p_inode1, old_dent, err1, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar) ∧ mkinode(m, md, true, m1, m2, m3) = p_inode0 ∧ mkinode(m0, md0, true, 1, m5, m6) = p_inode1 ∧ mkdentry(str, m0) = old_dent ∧ err0 = err1), m = 0, m0 = ROOT_INO, m0 = 0, m2 = 0, m3 = 0, m1 = 0 ∧ m ≠ ROOT_INO

Rule argument

spec: node name: elim-03 seq: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)) subst: [nd, key, md, boolvar, m, m0, m1] → [fs[ri[inodekey(m0)]], key1, md2, boolvar1, m4, m5, m6]

Additional information

Used simplifier rules: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)); (elim) Used terms: fs[ri[inodekey(m0)]], key1, md2, boolvar1, m4, m5, m6