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Proof step 72 from proof inv-write (previous step)

VFS_PAGE_SIZE = n1 + (m1 - m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE), of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs), content0), err = ESUCCESS, files0 = files1 [m, mkfile (m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 - m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, n1)] upto m1) ], ino4 = 0, dom of < ino3, afs-cons(dirs, files1), of-cons(of, dirs, files1), m ∈ files1, m1 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, n0 ≤ # buf0, m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE ≤ m1 ⊦ [vfs_write_loop# (m0, 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 - m1 / VFS_PAGE_SIZE * 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 - m1 / VFS_PAGE_SIZE * 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 - m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, n1)] upto m1) ] [m ] .size:= m1 ] [m ] .meta:= md ] [m ] .size), m0 + n0, buf0, dirs ; ino4, err, files0, asynced); if ino4 ≠ 0 then err := ESUCCESS; dirs1 := dirs; 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)), m1 - m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE = 0, 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 73:
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, files0 = files1 [m, mkfile (m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, m1 - m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, n1)] upto m1) ], ino4 = 0, m1 ≠ m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, n0 ≠ 0, dom of < ino3, afs-cons(dirs, files1), of-cons(of, dirs, files1), fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n0 ≤ # buf0 ⊦ [vfs_write_loop# (m0, 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 - m1 / VFS_PAGE_SIZE * 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 - m1 / VFS_PAGE_SIZE * 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 - m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, n1)] upto m1) ] [m ] .size:= m1 ] [m ] .meta:= md ] [m ] .size), m0 + n0, buf0, dirs ; ino4, err, files0, asynced); if ino4 ≠ 0 then err := ESUCCESS; dirs1 := dirs; 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

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ n → (n - m = 0 ↔ n = m); (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%n ≠ 0 ⊦ m / n * n ≤ m; (s)