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Proof step 97 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) ⊦ 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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: at-dels-ro-nodata seq: ⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key] subst: [key, ks, ri] → [inodekey(ino), orphans(fs0, ri1), ri1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ inodekey(ino) ∈ ri → (inodekey(ino) ∈ ri ⊖ ro ↔ ¬ inodekey(ino) ∈ ro); (s)%⊦ key ∈ orphans(fs, ri) ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ ¬ inodekey(m).data?; (s)%⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks); (ws) Used terms: inodekey(ino), orphans(fs0, ri1), ri1