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Proof step 81 from proof recovery (previous step)

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))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 82:
⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key]
Proof step 83:
fs0[ri1[inodekey(ino)]].directory, 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 ⊦ inodekey(ino).data?, inodekey(ino) ∈ orphans(fs0, ri1), (fs0[ri1[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ↔ 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[inodekey(ino)]].size, fs0[ri1[inodekey(ino)]].meta, fs0[ri1[inodekey(ino)]].nlink, fs0[ri1[inodekey(ino)]].nsubdirs, abs-children(ino, fs0, ri1 ⊖ orphans(fs0, ri1)))), fs0[ri1[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO

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: ⊦ 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) Used terms: inodekey(ino), orphans(fs0, ri1), ri1