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Proof step 101 from proof refine-writepage (previous step)

# buf = VFS_PAGE_SIZE, orphans(fs1, ri).inodes?, fo.inodes?, 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 (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])) = abs-keys(orphans(fs1, ri)), fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 102:
⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) → orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(orphans(fs, ri))
Proof step 103:
# 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])]), 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 ⊦ orphans (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])) = abs-keys(orphans(fs1, ri)), fs1[ri[inodekey(m)]].directory, 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])), adr1 ∈ fs1
Proof step 108:
# 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 ⊦ abs-keys(orphans(fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1])) = abs-keys(orphans(fs1, ri)), fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1

Rule argument

spec: aubifs-abs name: abs-orphans seq: ⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) → orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(orphans(fs, ri)) subst: [ri, fs] → [ri[datakey(m, pageno), adr1], fs1[adr1, datanode(datakey(m, pageno), buf)]] flags: <all paths>

Additional information

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