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Proof step 454 from proof inv-write (previous step)

VFS_PAGE_SIZE = n1 + (m0 + ino0) % VFS_PAGE_SIZE, files[m] = mkfile(m2, md0, m3, content), files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), buf = copy(buf0, ino0, zeropage, (m0 + ino0) % VFS_PAGE_SIZE, min(m0 + n0 - m0 + ino0, n1)), err = ESUCCESS, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), pageno = (m0 + ino0) / VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files0), afs-cons(dirs, files), of-cons(of, dirs, files0), of-cons(of, dirs, files), fd ∈ of, m ∈ files0, ino0 + min(m0 + n0 - m0 + ino0, n1) ≤ # buf0, (m0 + ino0) % VFS_PAGE_SIZE + min(m0 + n0 - m0 + ino0, n1) ≤ # zeropage, ino0 + min(n0 - ino0, n1) ≤ # buf0, (m0 + ino0) % VFS_PAGE_SIZE + min(n0 - ino0, n1) ≤ VFS_PAGE_SIZE, ino0 ≤ n0, n0 ≤ # buf0, ino0 ≤ # buf0, m0 + n0 ≥ m0 + ino0 ⊦ [if pre-writepage(inode, pageno, buf, dirs, files) then {{files[inode.ino].content[pageno] := buf; err := ESUCCESS} or fail#(; ; err); asynced := ?} else abort; if err = ESUCCESS then ino3 := ino0 + min(m0 + n0 - m0 + ino0, n1)] (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), VFS_PAGE_SIZE = 0, min(n0 - ino0, n1) = 0, n0 = 0, (m0 + ino0) / VFS_PAGE_SIZE ∈ content, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 455:
VFS_PAGE_SIZE = n1 + (m0 + ino0) % VFS_PAGE_SIZE, of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m1, md, # links(m, dirs), content0), files[m] = mkfile(m2, md0, m3, content), buf = copy(buf0, ino0, zeropage, (m0 + ino0) % VFS_PAGE_SIZE, min(m0 + n0 - m0 + ino0, n1)), err = ESUCCESS, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), pageno = (m0 + ino0) / VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files), afs-cons(dirs, files0), of-cons(of, dirs, files), of-cons(of, dirs, files0), m ∈ files0, fd ∈ of, ino0 ≤ # buf0, n0 ≤ # buf0, ino0 ≤ n0, (m0 + ino0) % VFS_PAGE_SIZE + min(n0 - ino0, n1) ≤ VFS_PAGE_SIZE, ino0 + min(n0 - ino0, n1) ≤ # buf0, (m0 + ino0) % VFS_PAGE_SIZE + min(m0 + n0 - m0 + ino0, n1) ≤ # zeropage, ino0 + min(m0 + n0 - m0 + ino0, n1) ≤ # buf0, m0 + n0 ≥ m0 + ino0 ⊦ [{files[inode.ino].content[pageno] := buf; err := ESUCCESS} or fail#(; ; err); asynced := ?; if err = ESUCCESS then ino3 := ino0 + min(m0 + n0 - m0 + ino0, n1)] (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), VFS_PAGE_SIZE = 0, min(n0 - ino0, n1) = 0, n0 = 0, (m0 + ino0) / VFS_PAGE_SIZE ∈ content, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ m + n - n + n1 = m - n1; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%⊦ 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)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)% ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s)% ⊦ # zeropage = VFS_PAGE_SIZE; (s)