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Proof step 119 from proof refine-evict (previous step)

fs[ri[inodekey(ino0)]].nlink = 0, 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, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m) ∈ ri, inodekey(ino0) ∈ ri, asynced → boolvar, fs[ri[inodekey(m)]].directory ∧ m2 = fs[ri[inodekey(m)]].size ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar0 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m1 = 0 ∧ ¬ boolvar0 ⊦ # links(ino0, fs, ri) = 0, ino0 = ROOT_INO, links(ino0, fs, ri) = ∅, m = ROOT_INO

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 120:
⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0)
Proof step 121:
fs[ri[inodekey(ino0)]].nlink = 0, 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), inodekey(ino0) ∈ ri, inodekey(m) ∈ ri, asynced → boolvar, fs[ri[inodekey(m)]].directory ∧ m2 = fs[ri[inodekey(m)]].size ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar0 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m1 = 0 ∧ ¬ boolvar0 ⊦ # links(ino0, fs, ri) = 0, ino0 = ROOT_INO, m = ROOT_INO, ∀ key. key ∈ links(ino0, fs, ri) ↔ key ∈ ∅

Rule argument

spec: set-basic, inst: node-index name: Extension seq: ⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0) subst: [ks0, ks] → [∅, links(ino0, fs, ri)] flags: <all paths>

Additional information

Used terms: ∅, links(ino0, fs, ri)