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Proof step 31 from proof refine-writepage (previous step)

# buf = VFS_PAGE_SIZE, boolvar ↔ boolvar2, adr = adr1, dirs = abs-dirs(fs1, ri), files = abs-files(fs1, ri), fs = fs1[adr1, datanode(datakey(m, pageno), buf)], key = datakey(m, pageno), log = log0 + adr1 ', ro = orphans(fs1, ri), ro0 = orphans(fs1, ri), fo.inodes?, orphans(fs1, ri).inodes?, 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(fi), ri-inj(ri), ubifs-cons(fs1, ri, orphans(fs1, ri), fi, fo, log0), inodekey(m) ∈ ri, asynced → boolvar0 ⊦ ⟪if ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr]) then ri[key] := adr else abort⟫ ⟨afs_writepage#(mkinode(m, md, boolvar1, m0, m1, m2), pageno, buf, dirs; err0, files; asynced)⟩ ( dirs = abs-dirs(fs1[adr1, datanode(datakey(m, pageno), buf)], ri) ∧ files = abs-files(fs1[adr1, datanode(datakey(m, pageno), buf)], ri) ∧ orphans(abs-dirs(fs1[adr1, datanode(datakey(m, pageno), buf)], ri), abs-files(fs1[adr1, datanode(datakey(m, pageno), buf)], ri)) = abs-keys(ro0) ∧ (asynced → boolvar2) ∧ ESUCCESS = err0), fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 32:
# buf = VFS_PAGE_SIZE, boolvar ↔ boolvar2, adr = adr1, dirs = abs-dirs(fs1, ri), files = abs-files(fs1, ri), fs = fs1[adr1, datanode(datakey(m, pageno), buf)], key = datakey(m, pageno), log = log0 + adr1 ', ro = orphans(fs1, ri), ro0 = orphans(fs1, ri), orphans(fs1, ri).inodes?, fo.inodes?, 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, asynced → boolvar0 ⊦ ⟪ri[key] := adr⟫ ⟨afs_writepage#(mkinode(m, md, boolvar1, m0, m1, m2), pageno, buf, dirs; err0, files; asynced)⟩ ( dirs = abs-dirs(fs1[adr1, datanode(datakey(m, pageno), buf)], ri) ∧ files = abs-files(fs1[adr1, datanode(datakey(m, pageno), buf)], ri) ∧ orphans(abs-dirs(fs1[adr1, datanode(datakey(m, pageno), buf)], ri), abs-files(fs1[adr1, datanode(datakey(m, pageno), buf)], ri)) = abs-keys(ro0) ∧ (asynced → boolvar2) ∧ ESUCCESS = err0), fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ key-cons(datakey(ino, n), nd) ↔ nd.data? ∧ nd.key = datakey(ino, n); (s)% ⊦ datanode(key, buf).data?; (s)% ⊦ datanode(key, buf).key = key; (s)% ⊦ adr ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → adr ∈ fs; (ss)