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Proof step 81 from proof inv-write (previous step)

m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs), content0), err = ESUCCESS, files = files1[m, mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1)], ino = 0, ino0 = m0 + n0, ino1 = m0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), ¬ isdir, m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, n0 ≠ 0, n2 ≠ 0, dom of < ino3, afs-cons(dirs, files1), of-cons(of, dirs, files1), m ∈ files1, m1 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, n0 ≤ # buf0, n2 + n1 ≤ VFS_PAGE_SIZE ⊦ [while err = ESUCCESS ∧ ¬ isdir do vfs_write_block#(ino1, inode, buf0, ino0, dirs; ino, isdir, err, files, asynced); ino4 := ino; if ino4 ≠ 0 then err := ESUCCESS; dirs1 := dirs; files0 := files; if err = ESUCCESS then let ino0 = (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files1 [m, files1 [m, files1 [m, mkfile (m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 % VFS_PAGE_SIZE, n1)] upto m1) ] [m ] .size:= m1 ] [m ] .meta:= md ] [m ] .meta, false, files1 [m, files1 [m, files1 [m, mkfile (m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 % VFS_PAGE_SIZE, n1)] upto m1) ] [m ] .size:= m1 ] [m ] .meta:= md ] [m ] .nlink, 0, files1 [m, files1 [m, files1 [m, mkfile (m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 % VFS_PAGE_SIZE, n1)] upto m1) ] [m ] .size:= m1 ] [m ] .meta:= md ] [m ] .size) ) .size in {n0 := ino4, ino1 := m0 + ino4; if ino4 ≠ 0 ∧ ino0 < ino1 then {inode0 := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files1 [m, files1 [m, files1 [m, mkfile (m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 % VFS_PAGE_SIZE, n1)] upto m1) ] [m ] .size:= m1 ] [m ] .meta:= md ] [m ] .meta, false, files1 [m, files1 [m, files1 [m, mkfile (m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 % VFS_PAGE_SIZE, n1)] upto m1) ] [m ] .size:= m1 ] [m ] .meta:= md ] [m ] .nlink, 0, files1 [m, files1 [m, files1 [m, mkfile (m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 % VFS_PAGE_SIZE, n1)] upto m1) ] [m ] .size:= m1 ] [m ] .meta:= md ] [m ] .size) ) .size:= ino1; afs_check_commit#(dirs, files0; err; asynced); if err = ESUCCESS then afs_write_inode#(inode0; err, dirs, files0; asynced)}; if err ≠ ESUCCESS then n0 := (m0 ≤ ino0 ⊃ ino0 - m0;0), err := ESUCCESS; of[fd].pos := m0 + n0}] (dirs1 = dirs → of-cons(of, dirs, files0) ∧ dom of < ino3 ∧ afs-cons(dirs, files0)), mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule invariant right

And obtained the following new goals

Proof step 82:
m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files1[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), err = ESUCCESS, files = files1[m, mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1)], ino = 0, ino0 = m0 + n0, ino1 = m0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), ¬ isdir, m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files1), of-cons(of, dirs, files1), fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n2 + n1 ≤ VFS_PAGE_SIZE, n0 ≤ # buf0 ⊦ n0 = 0, n2 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, of-cons(of, dirs, files) ∧ dom of < ino3 ∧ afs-cons(dirs, files)
Proof step 95:
m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files1[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), err = ESUCCESS, err0 = ESUCCESS, files0 = files1[m, mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1)], ino0 = m0 + n0, ino1 = m0, ino2 = 0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), ¬ isdir, ¬ isdir0, m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files1), afs-cons(dirs, files), of-cons(of, dirs, files1), of-cons(of, dirs, files), fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n2 + n1 ≤ VFS_PAGE_SIZE, n0 ≤ # buf0 ⊦ [vfs_write_block#(ino1, inode, buf0, ino0, dirs; ino, isdir, err, files, asynced)] (of-cons(of, dirs, files) ∧ dom of < ino3 ∧ afs-cons(dirs, files)), n0 = 0, n2 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW
Proof step 211:
m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files1[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), err0 = ESUCCESS, files0 = files1[m, mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1)], ino0 = m0 + n0, ino1 = m0, ino2 = 0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), ¬ isdir0, m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files1), afs-cons(dirs, files), of-cons(of, dirs, files1), of-cons(of, dirs, files), fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n2 + n1 ≤ VFS_PAGE_SIZE, n0 ≤ # buf0 ⊦ [ino4 := ino; if ino4 ≠ 0 then err := ESUCCESS; dirs1 := dirs; files0 := files; if err = ESUCCESS then let ino0 = (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files1 [m, files1 [m, files1 [m, mkfile (m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 % VFS_PAGE_SIZE, n1)] upto m1) ] [m ] .size:= m1 ] [m ] .meta:= md ] [m ] .meta, false, files1 [m, files1 [m, files1 [m, mkfile (m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 % VFS_PAGE_SIZE, n1)] upto m1) ] [m ] .size:= m1 ] [m ] .meta:= md ] [m ] .nlink, 0, files1 [m, files1 [m, files1 [m, mkfile (m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 % VFS_PAGE_SIZE, n1)] upto m1) ] [m ] .size:= m1 ] [m ] .meta:= md ] [m ] .size) ) .size in {n0 := ino4, ino1 := m0 + ino4; if ino4 ≠ 0 ∧ ino0 < ino1 then {inode0 := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files1 [m, files1 [m, files1 [m, mkfile (m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 % VFS_PAGE_SIZE, n1)] upto m1) ] [m ] .size:= m1 ] [m ] .meta:= md ] [m ] .meta, false, files1 [m, files1 [m, files1 [m, mkfile (m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 % VFS_PAGE_SIZE, n1)] upto m1) ] [m ] .size:= m1 ] [m ] .meta:= md ] [m ] .nlink, 0, files1 [m, files1 [m, files1 [m, mkfile (m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 % VFS_PAGE_SIZE, n1)] upto m1) ] [m ] .size:= m1 ] [m ] .meta:= md ] [m ] .size) ) .size:= ino1; afs_check_commit#(dirs, files0; err; asynced); if err = ESUCCESS then afs_write_inode#(inode0; err, dirs, files0; asynced)}; if err ≠ ESUCCESS then n0 := (m0 ≤ ino0 ⊃ ino0 - m0;0), err := ESUCCESS; of[fd].pos := m0 + n0}] (dirs1 = dirs → of-cons(of, dirs, files0) ∧ dom of < ino3 ∧ afs-cons(dirs, files0)), n0 = 0, n2 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, err = ESUCCESS ∧ ¬ isdir

Rule argument

fma: of-cons(of, dirs, files) ∧ dom of < ino3 ∧ afs-cons(dirs, files) pos: right 1

Additional information

Used formulas: of-cons(of, dirs, files) ∧ dom of < ino3 ∧ afs-cons(dirs, files)