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Proof step 50 from proof refine-writepage (previous step)

# 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 ⊦ fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1, ( inodekey(ino) ∈ ri[datakey(m, pageno), adr1] ∧ (adr1 = ri[inodekey(ino)] ⊃ datanode(datakey(m, pageno), buf);fs1[ri[inodekey(ino)]]).directory ↔ inodekey(ino) ∈ ri ∧ fs1[ri[inodekey(ino)]].directory) ∧ ( inodekey(ino) ∈ ri[datakey(m, pageno), adr1] ∧ (adr1 = ri[inodekey(ino)] ⊃ datanode(datakey(m, pageno), buf);fs1[ri[inodekey(ino)]]).directory → 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)))

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 51:
# 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 ⊦ inodekey(ino) = datakey(m, pageno), fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1, ( inodekey(ino) ∈ ri[datakey(m, pageno), adr1] ∧ (adr1 = ri[inodekey(ino)] ⊃ datanode(datakey(m, pageno), buf);fs1[ri[inodekey(ino)]]).directory ↔ inodekey(ino) ∈ ri ∧ fs1[ri[inodekey(ino)]].directory) ∧ ( inodekey(ino) ∈ ri[datakey(m, pageno), adr1] ∧ (adr1 = ri[inodekey(ino)] ⊃ datanode(datakey(m, pageno), buf);fs1[ri[inodekey(ino)]]).directory → 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)))

Rule argument

fma: inodekey(ino) = datakey(m, pageno)

Additional information

Used simplifier rules: ⊦ inodekey(m) ≠ datakey(m0, m1); (s) Used formulas: inodekey(ino) = datakey(m, pageno)