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Proof step 58 from proof refine-writepage (previous step)

# buf = VFS_PAGE_SIZE, fs1[ri[inodekey(ino)]].directory, 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(ino) ∈ ri, inodekey(m) ∈ ri, asynced0 → boolvar0 ⊦ abs-dirs(fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1])[ino] = mkdir (fs1[ri[inodekey(ino)]].size, fs1[ri[inodekey(ino)]].meta, fs1[ri[inodekey(ino)]].nlink, fs1[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs1, ri)), adr1 = ri[inodekey(ino)], fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 59:
⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri)
Proof step 60:
# buf = VFS_PAGE_SIZE, fs1[ri[inodekey(ino)]].directory, fs1[adr1, datanode(datakey(m, pageno), buf)][ri[datakey(m, pageno), adr1][inodekey(ino)]].directory, 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, inodekey(ino) ∈ ri, inodekey(ino) ∈ ri[datakey(m, pageno), adr1], asynced0 → boolvar0 ⊦ abs-dir(ino, fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1]) = mkdir (fs1[ri[inodekey(ino)]].size, fs1[ri[inodekey(ino)]].meta, fs1[ri[inodekey(ino)]].nlink, fs1[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs1, ri)), adr1 = ri[inodekey(ino)], fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1

Rule argument

spec: aubifs-abs name: at-dirs seq: ⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri) subst: [ino, ri, fs] → [ino, ri[datakey(m, pageno), adr1], fs1[adr1, datanode(datakey(m, pageno), buf)]] flags: <all paths>

Additional information

Used simplifier rules: at-ri: ⊦ ri[key, adr][key0] = (key = key0 ⊃ adr;ri[key0]);% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (ws) Used terms: ino, ri[datakey(m, pageno), adr1], fs1[adr1, datanode(datakey(m, pageno), buf)]