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Proof step 2 from proof refine-writepage (previous step)

dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), orphans(dirs, files) = abs-keys(ro), fo.inodes?, ro.inodes?, afs-cons(dirs, files), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), pre-writepage(inode, pageno, buf, dirs, files), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), asynced → boolvar ⊦ ⟪aubifs_writepage#(inode, pageno, buf, fi, ro, fo; err, ri, fs, log, boolvar)⟫ ⟨afs_writepage#(inode, pageno, buf, dirs; err0, files; asynced)⟩ ((dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(dirs, files) = abs-keys(ro) ∧ (asynced → boolvar)) ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# buf = VFS_PAGE_SIZE, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), ro = orphans(fs, ri), fo.inodes?, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(inode.ino) ∈ ri, ¬ fs[ri[inodekey(inode.ino)]].directory, asynced → boolvar ⊦ ⟪aubifs_writepage#(inode, pageno, buf, fi, orphans(fs, ri), fo; err, ri, fs, log, boolvar)⟫ ⟨afs_writepage#(inode, pageno, buf, dirs; err0, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (asynced → boolvar) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ pre-writepage(inode, n, buf, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ # buf = VFS_PAGE_SIZE; (s)%⊦ ro.inodes? → (abs-keys(ro) = abs-keys(orphans(fs, ri)) ↔ ro = orphans(fs, ri)); (s)%⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) → orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(orphans(fs, ri)); (s)