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Proof step 60 from proof refine-writepage (previous step)

# 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
# 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 ⊦ adr1 = ri[inodekey(ino)], fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1, (dentrykey(ino, str) ∈ ri → dentrykey(ino, str) ∈ ri[datakey(m, pageno), adr1]) ∧ ( dentrykey(ino, str) ∈ ri → fs1[ri[dentrykey(ino, str)]].ino = (adr1 = ri[dentrykey(ino, str)] ⊃ datanode(datakey(m, pageno), buf);fs1[ri[dentrykey(ino, str)]]).ino)

Rule argument

Additional information

Used simplifier rules: at-ri: ⊦ ri[key, adr][key0] = (key = key0 ⊃ adr;ri[key0]);%mkdir-inj: ⊦ mkdir(n, md, m, n0, entries0) = mkdir(n, md, m, n0, entries1) ↔ entries0 = entries1;% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (las)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s)% ⊦ datakey(m, m0) ≠ dentrykey(m1, str); (s)% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (ws)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)%⊦ entries = abs-children(ino, fs, ri) ↔ (∀ str. (str ∈ entries ↔ dentrykey(ino, str) ∈ ri) ∧ ( str ∈ entries → entries[str] = fs[ri[dentrykey(ino, str)]].ino)); (ss)% ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)