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Proof step 12 from proof valid-parent-ino-precond (previous step)

abs-keys(ro) = abs-keys(orphans(fs, ri)), fs[ri[inodekey(m)]].directory, ro.inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), log-cons(log, fs), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(m) ∈ ri, inodekey(m) ∈ ro ⊦ # links(m, abs-dirs(fs, ri)) = 0, # ro = 0, links(m, abs-dirs(fs, ri)) = ∅, ro = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ ns = ns0 ↔ (∀ ino. ino ∈ ns ↔ ino ∈ ns0)
Proof step 14:
fs[ri[inodekey(m)]].directory, fo.inodes?, ro.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), log-cons(log, fs), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(m) ∈ ro, inodekey(m) ∈ ri, ∀ ino. ino ∈ abs-keys(ro) ↔ ino ∈ abs-keys(orphans(fs, ri)) ⊦ # ro = 0, # links(m, abs-dirs(fs, ri)) = 0, links(m, abs-dirs(fs, ri)) = ∅, ro = ∅

Rule argument

spec: set-basic, inst: dir-heap-refset name: Extension seq: ⊦ ns = ns0 ↔ (∀ ino. ino ∈ ns ↔ ino ∈ ns0) subst: [ns0, ns] → [abs-keys(orphans(fs, ri)), abs-keys(ro)] flags: <all paths>

Additional information

Used terms: abs-keys(orphans(fs, ri)), abs-keys(ro)