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Proof step 32 from proof write-term (previous step)

files[m] = mkfile(m1, md, m2, content), of[fd] = mkfile(m, mode, m0), buf-opt = none, dirs0 = dirs, err = ESUCCESS, inode = mkinode(m, md, false, m2, 0, m1), n ≠ 0, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of, n ≤ # buf ⊦ ⟪afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files, asynced); ino0 := 0; if err = ESUCCESS then vfs_write_loop#(m0, inode, m0 + n, buf, dirs; ino0, err, files, asynced); if ino0 ≠ 0 then err := ESUCCESS; if err = ESUCCESS then let ino = inode.size in {n := ino0, ino1 := m0 + ino0; if ino0 ≠ 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 n := (m0 ≤ ino ⊃ ino - m0;0), err := ESUCCESS; of[fd].pos := m0 + n}⟫ (dirs0 = dirs), mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule insert program lemma

And obtained the following new goals

Proof step 33:
afs-cons(dirs, files), pre-truncate(inode, n, pageno, buf-opt, dirs, files) ⊦ ⟪afs_truncate#(n, pageno; buf-opt, inode, asynced, err, dirs, files, asynced0)⟫ afs-cons(dirs, files)
Proof step 34:
of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, m2, content), buf-opt = none, dirs0 = dirs, err = ESUCCESS, inode = mkinode(m, md, false, m2, 0, m1), n0 = m1, pageno0 = m1 / VFS_PAGE_SIZE, afs-cons(dirs, files), of-cons(of, dirs, files), pre-truncate(inode, m1, m1 / VFS_PAGE_SIZE, buf-opt, dirs, files), fd ∈ of, n ≤ # buf ⊦ [afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files, asynced)] ( afs-cons(dirs, files) → ⟪ino0 := 0; if err = ESUCCESS then vfs_write_loop#(m0, inode, m0 + n, buf, dirs; ino0, err, files, asynced); if ino0 ≠ 0 then err := ESUCCESS; if err = ESUCCESS then let ino = inode.size in {n := ino0, ino1 := m0 + ino0; if ino0 ≠ 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 n := (m0 ≤ ino ⊃ ino - m0;0), err := ESUCCESS; of[fd].pos := m0 + n}⟫ (dirs0 = dirs)), n = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

spec: afs-asm name: inv-truncate seq: afs-cons(dirs, files), pre-truncate(inode, n, pageno, buf-opt, dirs, files) ⊦ ⟪afs_truncate# (n, pageno ; buf-opt, inode, asynced, err, dirs, files, asynced0)⟫ afs-cons(dirs, files) subst: [pageno, n, asynced0, files, dirs, err, asynced, inode, buf-opt] → [m1 / VFS_PAGE_SIZE, m1, asynced, files, dirs, err, isdir, inode, buf-opt] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 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)%⊦ 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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ ¬ none.some?; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)