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Proof step 39 from proof inv-write (previous step)

of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, m2, content), buf-opt = none, dirs1 = dirs, err = ESUCCESS, ino = 0, ino0 = 0, inode = mkinode(m, md, false, m2, 0, m1), n = m1, pageno = m1 / VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files), of-cons(of, dirs, files), pre-truncate(inode, n, pageno, buf-opt, dirs, files), fd ∈ of, n0 ≤ # buf ⊦ [afs_truncate_internal#(n, pageno; inode, buf-opt, ino0, ino, isdir, err, dirs, files; asynced); ino4 := 0; if err = ESUCCESS then vfs_write_loop#(m0, inode, m0 + n0, buf, dirs; ino4, err, files, asynced); if ino4 ≠ 0 then err := ESUCCESS; if err = ESUCCESS then let ino = inode.size in {n0 := ino4, ino1 := m0 + ino4; if ino4 ≠ 0 ∧ ino < ino1 then {inode.size := ino1; afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_write_inode#(inode; err, dirs, files; asynced)}; if err ≠ ESUCCESS then n0 := (m0 ≤ ino ⊃ ino - m0;0), err := ESUCCESS; of[fd].pos := m0 + n0}] (dirs1 = dirs → of-cons(of, dirs, files) ∧ dom of < ino3 ∧ afs-cons(dirs, files)), VFS_PAGE_SIZE = 0, n0 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, # links(m, dirs), content), buf-opt = none, dirs1 = dirs, err = ESUCCESS, ino = 0, ino0 = 0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), n0 ≠ 0, dom of < ino3, afs-cons(dirs, files), of-cons(of, dirs, files), m ∈ files, fd ∈ of, n0 ≤ # buf ⊦ [afs_truncate_internal#(m1, m1 / VFS_PAGE_SIZE; inode, buf-opt, ino0, ino, isdir, err, dirs, files; asynced); ino4 := 0; if err = ESUCCESS then vfs_write_loop#(m0, inode, m0 + n0, buf, dirs; ino4, err, files, asynced); if ino4 ≠ 0 then err := ESUCCESS; if err = ESUCCESS then let ino = inode.size in {n0 := ino4, ino1 := m0 + ino4; if ino4 ≠ 0 ∧ ino < ino1 then {inode.size := ino1; afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_write_inode#(inode; err, dirs, files; asynced)}; if err ≠ ESUCCESS then n0 := (m0 ≤ ino ⊃ ino - m0;0), err := ESUCCESS; of[fd].pos := m0 + n0}] (dirs1 = dirs → of-cons(of, dirs, files) ∧ dom of < ino3 ∧ afs-cons(dirs, files)), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ ¬ none.some?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)%⊦ pre-truncate(inode, n, pageno, buf-opt, dirs, files) ↔ valid-file-inode(inode, dirs, files) ∧ pageno = inode.size / VFS_PAGE_SIZE ∧ (buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE); (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)