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Proof step 408 from proof refine-rename-new-keep-parent (previous step)

boolvar2 ↔ boolvar, adr4 = adr1, dirs = abs-dirs(fs, ri), err = ENOSPC, files = abs-files(fs, ri), m = fs[ri[dentrykey(m3, str)]].ino, m4 = fs[ri[inodekey(m3)]].nlink, m5 = fs[ri[inodekey(m3)]].nsubdirs, m6 = fs[ri[inodekey(m3)]].size, nd = inodenode(inodekey(m3), md0, true, m4, m5, m6), nd0 = dentrynode(dentrykey(m3, str0), old_dent.ino), nd1 = dentrynode(dentrykey(m3, old_dent.name), 0), new_dent = negdentry(str0), new_dent_inode0 = new_dent_inode, new_inode = mkinode(m3, md0, true, m4, m5, m6), old_dent = mkdentry(str, fs[ri[dentrykey(m3, str)]].ino), old_dent0 = mkdentry(str, m), old_dent1 = negdentry(str0), old_dent_inode = mkinode(m, md, boolvar1, m0, m1, m2), old_inode = mkinode(m3, md0, true, m4, m5, m6), old_parent_inode = mkinode(m3, md0, true, m4, m5, m6), ro = orphans(fs, ri), ro0 = orphans(fs, ri), old_dent.dentry?, fs[ri[inodekey(m3)]].directory, 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, ro0), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, ro0, fi, fo, log), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, ro0, fi, fo, log), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m3) ∈ ri, inodekey(fs[ri[dentrykey(m3, str)]].ino) ∈ ri, dentrykey(m3, str) ∈ ri, 1 ≤ fs[ri[inodekey(m3)]].size, boolvar1 → 1 ≤ fs[ri[inodekey(m3)]].nsubdirs, boolvar3 → boolvar0, ∀ adr1, adr2, adr3. ¬(new(adr1 ' + (adr2 ' + adr3), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ')), fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ ¬ boolvar1 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ boolvar1 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].size, fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].size ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∧ boolvar1 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1 ⊦ ⟨afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar3)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (boolvar3 → boolvar2) ∧ old_parent_inode = old_inode ∧ old_parent_inode = new_inode ∧ mkinode(m, md, boolvar1, m0, m1, m2) = old_dent_inode ∧ new_dent_inode0 = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0), fs[ri[inodekey(m3)]].size = 0, dentrykey(m3, str0) ∈ ri, fs[ri[inodekey(m3)]].nlink = 0 ∧ m3 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 409:
dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), new_dent_inode0 = new_dent_inode, new_inode = mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, fs[ri[inodekey(m3)]].nsubdirs, fs[ri[inodekey(m3)]].size), old_dent0 = mkdentry(str, fs[ri[dentrykey(m3, str)]].ino), old_dent1 = negdentry(str0), old_dent_inode = mkinode(fs[ri[dentrykey(m3, str)]].ino, md, boolvar1, m0, m1, m2), old_inode = mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, fs[ri[inodekey(m3)]].nsubdirs, fs[ri[inodekey(m3)]].size), fs[ri[inodekey(m3)]].size ≠ 0, fs[ri[inodekey(m3)]].directory, 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-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m3, str) ∈ ri, inodekey(fs[ri[dentrykey(m3, str)]].ino) ∈ ri, inodekey(m3) ∈ ri, 1 ≤ fs[ri[inodekey(m3)]].size, ¬ dentrykey(m3, str0) ∈ ri, boolvar3 → boolvar0, boolvar1 → 1 ≤ fs[ri[inodekey(m3)]].nsubdirs, ∀ adr, adr0, adr1. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr0 = adr1, fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].size ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∧ boolvar1 ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ ¬ boolvar1 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].directory ∧ boolvar1 ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str)]].ino)]].size, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO ⊦ ⟨afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar3)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (boolvar3 → boolvar2) ∧ mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, fs[ri[inodekey(m3)]].nsubdirs, fs[ri[inodekey(m3)]].size) = old_inode ∧ mkinode(m3, md0, true, fs[ri[inodekey(m3)]].nlink, fs[ri[inodekey(m3)]].nsubdirs, fs[ri[inodekey(m3)]].size) = new_inode ∧ mkinode(fs[ri[dentrykey(m3, str)]].ino, md, boolvar1, m0, m1, m2) = old_dent_inode ∧ new_dent_inode0 = new_dent_inode ∧ mkdentry(str, fs[ri[dentrykey(m3, str)]].ino) = old_dent0 ∧ negdentry(str0) = old_dent1 ∧ ENOSPC = err0), fs[ri[inodekey(m3)]].nlink = 0 ∧ m3 ≠ ROOT_INO

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)