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Proof step 80 from proof recovery (previous step)

orphans(fs0, ri1).inodes?, fo0.inodes?, afs-cons(abs-dirs(fs0, ri1), abs-files(fs0, ri1)), file-node-cons(fs0, ri1), file-node-cons(fs0, ri1 ⊖ orphans(fs0, ri1)), log-cons(log0, fs0), orphans-cons(fs0, ri1, orphans(fs0, ri1)), orphans-cons(fs0, ri1 ⊖ orphans(fs0, ri1), ∅), replay-safe(log0, fs0, fi0 ⊖ fo0), ri-inj(ri1), ri-inj(fi0), ri-inj(ri1 ⊖ orphans(fs0, ri1)), ubifs-cons(fs0, ri1, orphans(fs0, ri1), fi0, fo0, log0), ubifs-cons(fs0, ri1 ⊖ orphans(fs0, ri1), ∅, fi0, fo0, log0), ino ∈ abs-dirs(fs0, ri1) ⊦ ino ∈ abs-keys(orphans(fs0, ri1)), ( inodekey(ino) ∈ ri1 ∧ fs0[ri1[inodekey(ino)]].directory ∧ (fs0[ri1[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO) ↔ inodekey(ino) ∈ ri1 ⊖ orphans(fs0, ri1) ∧ fs0[(ri1 ⊖ orphans(fs0, ri1))[inodekey(ino)]].directory) ∧ ( inodekey(ino) ∈ ri1 ∧ fs0[ri1[inodekey(ino)]].directory ∧ (fs0[ri1[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO) → abs-dirs(fs0, ri1)[ino] = mkdir (fs0[(ri1 ⊖ orphans(fs0, ri1))[inodekey(ino)]].size, fs0[(ri1 ⊖ orphans(fs0, ri1))[inodekey(ino)]].meta, fs0[(ri1 ⊖ orphans(fs0, ri1))[inodekey(ino)]].nlink, fs0[(ri1 ⊖ orphans(fs0, ri1))[inodekey(ino)]].nsubdirs, abs-children(ino, fs0, ri1 ⊖ orphans(fs0, ri1))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 81:
fs0[ri1[inodekey(ino)]].directory, fo0.inodes?, orphans(fs0, ri1).inodes?, afs-cons(abs-dirs(fs0, ri1), abs-files(fs0, ri1)), file-node-cons(fs0, ri1 ⊖ orphans(fs0, ri1)), file-node-cons(fs0, ri1), log-cons(log0, fs0), orphans-cons(fs0, ri1 ⊖ orphans(fs0, ri1), ∅), orphans-cons(fs0, ri1, orphans(fs0, ri1)), replay-safe(log0, fs0, fi0 ⊖ fo0), ri-inj(ri1 ⊖ orphans(fs0, ri1)), ri-inj(fi0), ri-inj(ri1), ubifs-cons(fs0, ri1 ⊖ orphans(fs0, ri1), ∅, fi0, fo0, log0), ubifs-cons(fs0, ri1, orphans(fs0, ri1), fi0, fo0, log0), inodekey(ino) ∈ ri1 ⊦ fs0[ri1[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO, (fs0[ri1[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ↔ fs0[(ri1 ⊖ orphans(fs0, ri1))[inodekey(ino)]].directory) ∧ ( fs0[ri1[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO → mkdir (fs0[ri1[inodekey(ino)]].size, fs0[ri1[inodekey(ino)]].meta, fs0[ri1[inodekey(ino)]].nlink, fs0[ri1[inodekey(ino)]].nsubdirs, abs-children(ino, fs0, ri1)) = mkdir (fs0[(ri1 ⊖ orphans(fs0, ri1))[inodekey(ino)]].size, fs0[(ri1 ⊖ orphans(fs0, ri1))[inodekey(ino)]].meta, fs0[(ri1 ⊖ orphans(fs0, ri1))[inodekey(ino)]].nlink, fs0[(ri1 ⊖ orphans(fs0, ri1))[inodekey(ino)]].nsubdirs, abs-children(ino, fs0, ri1 ⊖ orphans(fs0, ri1))))

Rule argument

Additional information

Used simplifier rules: ⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)%⊦ inodekey(ino) ∈ ri → (inodekey(ino) ∈ ri ⊖ ro ↔ ¬ inodekey(ino) ∈ ro); (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ key ∈ orphans(fs, ri) ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO; (s)% ⊦ n ∈ abs-keys(ks) ↔ inodekey(n) ∈ ks; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)