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Proof step 769 from proof refine-rename-overwrite-reparent-file (previous step)

m12 + 1 = fs[ri[inodekey(m0)]].nlink, 0 = fs[ri[inodekey(m0)]].nsubdirs, 0 = fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m4)]] = inodenode(key1, md3, true, m1, m3, m6), fs[ri[dentrykey(m9, str)]] = dentrynode(key, m), fs[ri[dentrykey(m4, str0)]] = dentrynode(key0, m0), fs[ri[inodekey(m9)]] = inodenode(key2, md4, true, m7, m8, m14 + 1), dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), new_dent_inode = mkinode(m0, md0, false, m12 + 1, 0, m5), new_inode = mkinode(m4, md1, true, m1, m3, m6), old_dent0 = mkdentry(str, m), old_dent1 = mkdentry(str0, m0), old_dent_inode = mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2), old_inode = mkinode(m9, md2, true, m7, m8, m14 + 1), m0 ≠ ROOT_INO, m0 ≠ 0, m4 ≠ 0, m9 ≠ m4, m9 ≠ 0, fs[ri[inodekey(m)]].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), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m9) ∈ ri, ri[inodekey(m9)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m4)] ∈ fs, inodekey(m4) ∈ ri, ri[dentrykey(m4, str0)] ∈ fs, dentrykey(m4, str0) ∈ ri, ri[dentrykey(m9, str)] ∈ fs, dentrykey(m9, str) ∈ ri, ⌊err0⌋ , ¬ fs[ri[inodekey(m0)]].directory, ¬ fs[ri[inodekey(m)]].directory, m12 = 0 → links(m0, fs, ri) = ∅ ++ dentrykey(m4, str0), boolvar2 → boolvar0, links(m9, abs-dirs(fs, ri)) ≠ ∅ ∨ m9 = ROOT_INO, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO, m7 ≠ 0 ∨ m9 = ROOT_INO, m1 ≠ 0 ∨ m4 = ROOT_INO ⊦ ⟨afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err1, dirs, files; boolvar2)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (boolvar2 → boolvar1) ∧ mkinode(m9, md2, true, m7, m8, m14 + 1) = old_inode ∧ mkinode(m4, md1, true, m1, m3, m6) = new_inode ∧ mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2) = old_dent_inode ∧ mkinode(m0, md0, false, m12 + 1, 0, m5) = new_dent_inode ∧ mkdentry(str, m) = old_dent0 ∧ mkdentry(str0, m0) = old_dent1 ∧ err0 = err1), m1 = 0 ∧ m4 ≠ ROOT_INO, m7 = 0 ∧ m9 ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 770:
m12 + 1 = fs[ri[inodekey(m0)]].nlink, 0 = m11, 0 = fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m9)]] = inodenode(key2, md4, true, m7, m8, m14 + 1), fs[ri[dentrykey(m4, str0)]] = dentrynode(key0, m0), fs[ri[dentrykey(m9, str)]] = dentrynode(key, m), fs[ri[inodekey(m4)]] = inodenode(key1, md3, true, m1, m3, m6), fs[ri[inodekey(m)]] = inodenode(key3, md5, boolvar, m10, m11, m13), ¬ boolvar, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), new_dent_inode = mkinode(m0, md0, false, m12 + 1, 0, m5), new_inode = mkinode(m4, md1, true, m1, m3, m6), old_dent0 = mkdentry(str, m), old_dent1 = mkdentry(str0, m0), old_dent_inode = mkinode(m, md, false, m10, 0, m2), old_inode = mkinode(m9, md2, true, m7, m8, m14 + 1), fs[ri[inodekey(m)]].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), dentrykey(m9, str) ∈ ri, ri[dentrykey(m9, str)] ∈ fs, dentrykey(m4, str0) ∈ ri, ri[dentrykey(m4, str0)] ∈ fs, inodekey(m4) ∈ ri, ri[inodekey(m4)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m9)] ∈ fs, inodekey(m9) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, ⌊err0⌋ , boolvar2 → boolvar0, m12 = 0 → links(m0, fs, ri) = ∅ ++ dentrykey(m4, str0), m1 ≠ 0 ∨ m4 = ROOT_INO, m7 ≠ 0 ∨ m9 = ROOT_INO, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO, links(m9, abs-dirs(fs, ri)) ≠ ∅ ∨ m9 = ROOT_INO ⊦ ⟨afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err1, dirs, files; boolvar2)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (boolvar2 → boolvar1) ∧ mkinode(m9, md2, true, m7, m8, m14 + 1) = old_inode ∧ mkinode(m4, md1, true, m1, m3, m6) = new_inode ∧ mkinode(m, md, false, m10, 0, m2) = old_dent_inode ∧ mkinode(m0, md0, false, m12 + 1, 0, m5) = new_dent_inode ∧ mkdentry(str, m) = old_dent0 ∧ mkdentry(str0, m0) = old_dent1 ∧ err0 = err1), m0 = ROOT_INO, m0 = 0, m4 = 0, m9 = m4, m9 = 0, fs[ri[inodekey(m0)]].directory, m7 = 0 ∧ m9 ≠ ROOT_INO, m1 = 0 ∧ m4 ≠ 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(m)]], key3, md5, boolvar, m10, m11, m13]

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(m)]], key3, md5, boolvar, m10, m11, m13