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Proof step 109 from proof refine-writepage (previous step)

# buf = VFS_PAGE_SIZE, orphans(fs1, ri).inodes?, fo.inodes?, afs-cons (abs-dirs(fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1]), abs-files(fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1])), afs-cons (abs-dirs(fs1, ri), abs-files(fs1, ri)[m, mkfile(fs1[ri[inodekey(m)]].size, fs1[ri[inodekey(m)]].meta, fs1[ri[inodekey(m)]].nlink, abs-content(m, fs1, ri)[pageno, buf])]), afs-cons(abs-dirs(fs1, ri), abs-files(fs1, ri)), file-node-cons(fs1, ri), log-cons(log0, fs1), orphans-cons(fs1, ri, orphans(fs1, ri)), replay-cons-strong(fs1, ri, orphans(fs1, ri), fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs1, ri, orphans(fs1, ri), fi, fo, log0), inodekey(m) ∈ ri, asynced0 → boolvar0 ⊦ orphans(fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1]) = orphans(fs1, ri), fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 110:
⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0)
Proof step 111:
# buf = VFS_PAGE_SIZE, fo.inodes?, orphans(fs1, ri).inodes?, afs-cons(abs-dirs(fs1, ri), abs-files(fs1, ri)), afs-cons (abs-dirs(fs1, ri), abs-files(fs1, ri)[m, mkfile(fs1[ri[inodekey(m)]].size, fs1[ri[inodekey(m)]].meta, fs1[ri[inodekey(m)]].nlink, abs-content(m, fs1, ri)[pageno, buf])]), afs-cons (abs-dirs(fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1]), abs-files(fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1])), file-node-cons(fs1, ri), log-cons(log0, fs1), orphans-cons(fs1, ri, orphans(fs1, ri)), replay-cons-strong(fs1, ri, orphans(fs1, ri), fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs1, ri, orphans(fs1, ri), fi, fo, log0), inodekey(m) ∈ ri, asynced0 → boolvar0 ⊦ fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1, ∀ key. key ∈ orphans(fs1, ri) ↔ key ∈ orphans(fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1])

Rule argument

spec: set-basic, inst: node-index name: Extension seq: ⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0) subst: [ks, ks0] → [orphans(fs1, ri), orphans (fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1])] flags: <all paths>

Additional information

Used terms: orphans(fs1, ri), orphans (fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1])