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Proof step 16 from proof crash-neutral-truncate (previous step)

files[m] = mkfile(m1, md1, # links(m, dirs), content0), afs-cons(dirs, files), m ∈ files, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, ⟨let ino = m, content = content0, buf = ? in {old_ino0 := m2 % VFS_PAGE_SIZE, old_ino := min(n, m2); asynced0 := m2 ≤ n ∧ old_ino0 ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content ∨ buf-opt.some?); if asynced0 then {pageno := m2 / VFS_PAGE_SIZE; if buf-opt.some? then buf := buf-opt.buf else buf := files[ino].content[pageno]; buf := fill(buf, zero, old_ino0, VFS_PAGE_SIZE - old_ino0); content[pageno] := buf; buf-opt := some(buf)}; files1 := files[ino, files[ino].content:= (content upto old_ino)]; let new_inode = mkinode(m, md, false, # links(m, dirs), 0, m2) in {new_inode.size := n; dirs1 := dirs; dirs2 := dirs; dirs3 := dirs; afs_inode_sync#(new_inode; dirs, files1)}; inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files1[m].meta, false, files1[m].nlink, 0, files1[m].size) ); err := ESUCCESS}; asynced := ?⟩ (asynced ∧ dirs3 \ orphans(dirs3, files) = dirs \ orphans(dirs, files1) ∧ files \ orphans(dirs2, files) = files1 \ orphans(dirs, files1))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 17:
files[m] = mkfile(m1, md1, # links(m, dirs), content0), afs-cons(dirs, files), m ∈ files, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE ⊦ ⟨choose err0 with ⌊err0⌋ in err := err0; asynced := ?⟩ asynced, ⟨let ino = m, content = content0, buf = ? in {old_ino0 := m2 % VFS_PAGE_SIZE, old_ino := min(n, m2); asynced0 := m2 ≤ n ∧ old_ino0 ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content ∨ buf-opt.some?); if asynced0 then {pageno := m2 / VFS_PAGE_SIZE; if buf-opt.some? then buf := buf-opt.buf else buf := files[ino].content[pageno]; buf := fill(buf, zero, old_ino0, VFS_PAGE_SIZE - old_ino0); content[pageno] := buf; buf-opt := some(buf)}; files1 := files[ino, files[ino].content:= (content upto old_ino)]; let new_inode = mkinode(m, md, false, # links(m, dirs), 0, m2) in {new_inode.size := n; dirs1 := dirs; dirs2 := dirs; dirs3 := dirs; afs_inode_sync#(new_inode; dirs, files1)}; inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files1[m].meta, false, files1[m].nlink, 0, files1[m].size) ); err := ESUCCESS}; asynced := ?⟩ (asynced ∧ dirs3 \ orphans(dirs3, files) = dirs \ orphans(dirs, files1) ∧ files \ orphans(dirs2, files) = files1 \ orphans(dirs, files1))

Rule argument

pos: right 1

Additional information

Used simplifier rules: fail#(; ; ERR){choose ERR0 with ⌊ERR0⌋ in ERR := ERR0};