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Proof step 705 from proof refine-rename-overwrite-reparent-file (previous step)

m14 + 1 = fs[ri[inodekey(m9)]].size, m12 + 1 = fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink, boolvar1 ↔ boolvar, 0 = fs[ri[inodekey(fs[ri[dentrykey(m9, str)]].ino)]].nsubdirs, 0 = fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nsubdirs, adr1 = adr6, adr2 = adr7, adr6 = adr4, adr7 = adr5, adr8 = adr3, dirs = abs-dirs(fs, ri), err = ENOSPC, files = abs-files(fs, ri), m = fs[ri[dentrykey(m9, str)]].ino, m0 = fs[ri[inodekey(fs[ri[dentrykey(m9, str)]].ino)]].nlink, m1 = fs[ri[dentrykey(m4, str0)]].ino, m10 = fs[ri[inodekey(m9)]].nlink, m13 = m4, m6 = fs[ri[inodekey(m4)]].nlink, m7 = fs[ri[inodekey(m4)]].nsubdirs, m8 = fs[ri[inodekey(m4)]].size, n0 = fs[ri[inodekey(m9)]].nsubdirs, nd = inodenode(inodekey(new_dent.ino), md0, false, m12, 0, m5), nd0 = inodenode(inodekey(m4), md1, true, m6, m7, m8), nd1 = inodenode(inodekey(m9), md2, true, m10, n0, m14), nd2 = dentrynode(dentrykey(m4, new_dent.name), old_dent.ino), nd3 = dentrynode(dentrykey(m9, old_dent.name), 0), new_child_inode = mkinode(m1, md0, false, m12 + 1, 0, m5), new_dent = mkdentry(str0, fs[ri[dentrykey(m4, str0)]].ino), new_dent_inode = mkinode(m1, md0, false, m12 + 1, 0, m5), new_inode = mkinode(m4, md1, true, m6, m7, m8), old_dent = mkdentry(str, fs[ri[dentrykey(m9, str)]].ino), old_dent0 = mkdentry(str, m), old_dent1 = mkdentry(str0, m1), old_dent_inode = mkinode(m, md, false, m0, 0, m2), old_inode = mkinode(m9, md2, true, m10, n0, m14 + 1), old_parent_inode = mkinode(m9, md2, true, m10, n0, m14 + 1), ro = orphans(fs, ri), ro0 = orphans(fs, ri), new_dent.dentry?, old_dent.dentry?, fs[ri[inodekey(m4)]].directory, fs[ri[inodekey(m9)]].directory, orphans(fs, ri).inodes?, fo.inodes?, ro0.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), node-cons(nd3.key, nd3), node-cons(nd2.key, nd2), node-cons(nd1.key, nd1), node-cons(nd0.key, nd0), node-cons(nd.key, nd), orphans-cons(fs, ri, orphans(fs, ri)), orphans-cons(fs, ri, ro0), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), replay-cons-strong(fs, ri, ro0, fi, fo, log), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), ubifs-cons(fs, ri, ro0, fi, fo, log), inodekey(m9) ∈ ri, inodekey(m4) ∈ ri, dentrykey(m4, str0) ∈ ri, inodekey(fs[ri[dentrykey(m4, str0)]].ino) ∈ ri, dentrykey(m9, str) ∈ ri, inodekey(fs[ri[dentrykey(m9, str)]].ino) ∈ ri, boolvar2 → boolvar0, m12 = 0 → links(fs[ri[dentrykey(m4, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m4, str0), ∀ adr1, adr2, adr3, adr4, adr5. ¬(new(adr1 ' + adr2 ' + adr3 ' + (adr4 ' + adr5), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ' + adr4 ' + adr5 ')), fs[ri[inodekey(m4)]].nlink ≠ 0 ∨ m4 = ROOT_INO, fs[ri[inodekey(m9)]].nlink ≠ 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, err0, dirs, files; boolvar2)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (boolvar2 → boolvar1) ∧ old_parent_inode = old_inode ∧ mkinode(m13, md1, true, m6, m7, m8) = new_inode ∧ mkinode(m, md, false, m0, 0, m2) = old_dent_inode ∧ new_child_inode = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0), fs[ri[dentrykey(m4, str0)]].ino = ROOT_INO, m9 = m4, fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m9, str)]].ino)]].directory, fs[ri[inodekey(m9)]].nlink = 0 ∧ m9 ≠ ROOT_INO, fs[ri[inodekey(m4)]].nlink = 0 ∧ m4 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ abs-keys(orphans(fs0, ri0)) = abs-keys(orphans(fs, ri)) ↔ orphans(fs0, ri0) = orphans(fs, ri); (s)%⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) → orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(orphans(fs, ri)); (s)% ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ dups(adr ' + ax) ↔ adr ∈ ax ∨ dups(ax); (s)% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + adr = ax + adr '; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ node-cons(key0, dentrynode(key1, ino)) ↔ key0.dentry?; (s)% ⊦ dentrynode(key, m).key = key; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ mkdentry(str, m).ino = m; (s)