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Proof step 34 from proof refine-writepage (previous step)

# buf = VFS_PAGE_SIZE, files = abs-files(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, ¬ fs1[ri[inodekey(m)]].directory, ¬ adr1 ∈ fs1, asynced → boolvar0 ⊦ ⟨afs_writepage#(mkinode(m, md, boolvar1, m0, m1, m2), pageno, buf, abs-dirs(fs1, ri); err0, files; asynced)⟩ ( abs-dirs(fs1, ri) = abs-dirs(fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1]) ∧ files = abs-files(fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1]) ∧ 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)) ∧ (asynced → boolvar2) ∧ ESUCCESS = err0)

User applied rule insert program lemma

And obtained the following new goals

Proof step 35:
afs-cons(dirs, files), pre-writepage(inode, pageno, buf, dirs, files) ⊦ ⟪afs_writepage#(inode, pageno, buf, dirs; err, files; asynced)⟫ afs-cons(dirs, files)
Proof step 36:
# buf = VFS_PAGE_SIZE, buf0 = buf, dirs0 = abs-dirs(fs1, ri), files = abs-files(fs1, ri), inode0 = mkinode(m, md, boolvar1, m0, m1, m2), pageno0 = pageno, fo.inodes?, orphans(fs1, ri).inodes?, afs-cons(abs-dirs(fs1, ri), abs-files(fs1, ri)), afs-cons(abs-dirs(fs1, ri), files), file-node-cons(fs1, ri), log-cons(log0, fs1), orphans-cons(fs1, ri, orphans(fs1, ri)), pre-writepage(mkinode(m, md, boolvar1, m0, m1, m2), pageno, buf, abs-dirs(fs1, ri), files), 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 ⊦ ⟨afs_writepage#(mkinode(m, md, boolvar1, m0, m1, m2), pageno, buf, abs-dirs(fs1, ri); err0, files; asynced)⟩ ( afs-cons(dirs0, files) → abs-dirs(fs1, ri) = abs-dirs(fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1]) ∧ files = abs-files(fs1[adr1, datanode(datakey(m, pageno), buf)], ri[datakey(m, pageno), adr1]) ∧ 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)) ∧ (asynced → boolvar2) ∧ ESUCCESS = err0), fs1[ri[inodekey(m)]].directory, adr1 ∈ fs1

Rule argument

spec: afs-asm name: inv-writepage seq: afs-cons(dirs, files), pre-writepage(inode, pageno, buf, dirs, files) ⊦ ⟪afs_writepage# (inode, pageno, buf, dirs; err, files; asynced)⟫ afs-cons(dirs, files) subst: [dirs, buf, pageno, inode, files, err, asynced] → [abs-dirs(fs1, ri), buf, pageno, mkinode(m, md, boolvar1, m0, m1, m2), files, err0, asynced] flags: List([[1,0,0]])

Additional information

Used simplifier rules: ⊦ pre-writepage(inode, n, buf, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ # buf = VFS_PAGE_SIZE; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)