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Proof step 181 from proof write-term (previous step)

of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m2, md0, # links(m, dirs), content0), err = ESUCCESS, files = files0[m, mkfile(m2, md0, # links(m, dirs), content0 upto m2)], ino3 = 0, afs-cons(dirs, files0), afs-cons(dirs, files0[m, mkfile(m2, md0, # links(m, dirs), content0 upto m2)]), of-cons(of, dirs, files0), m ∈ files0, fd ∈ of, n0 ≤ # buf0 ⊦ ∀ ino3, err, files, asynced. m ∈ files ∧ # links(m, dirs) = files[m].nlink → ⟪if ino3 ≠ 0 then err := ESUCCESS; dirs0 := dirs; if err = ESUCCESS then let ino = m2 in {n0 := ino3, ino1 := m0 + ino3; if ino3 ≠ 0 ∧ ino < ino1 then {inode0 := mkinode(m, md0, false, # links(m, dirs), 0, ino1); afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_write_inode#(inode0; err, dirs, files; asynced)}; if err ≠ ESUCCESS then n0 := (m0 ≤ ino ⊃ ino - m0;0), err := ESUCCESS; of[fd].pos := m0 + n0}⟫ (dirs0 = dirs), n0 = 0, m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 182:
# links(m, dirs) = files1[m].nlink, files0[m] = mkfile(m2, md0, files1[m].nlink, content0), of[fd] = mkfile(m, mode, m0), n0 ≠ 0, afs-cons(dirs, files0[m, mkfile(m2, md0, files1[m].nlink, content0 upto m2)]), afs-cons(dirs, files0), of-cons(of, dirs, files0), m ∈ files1, fd ∈ of, m ∈ files0, n0 ≤ # buf0 ⊦ ⟪if ino ≠ 0 then err0 := ESUCCESS; dirs0 := dirs; if err0 = ESUCCESS then let ino0 = m2 in {n0 := ino, ino1 := m0 + ino; if ino ≠ 0 ∧ ino0 < ino1 then {inode0 := mkinode(m, md0, false, files1[m].nlink, 0, ino1); afs_check_commit#(dirs, files1; err0; asynced); if err0 = ESUCCESS then afs_write_inode#(inode0; err0, dirs, files1; asynced)}; if err0 ≠ ESUCCESS then n0 := (m0 ≤ ino0 ⊃ ino0 - m0;0), err0 := ESUCCESS; of[fd].pos := m0 + n0}⟫ (dirs0 = dirs), mode ≠ MODE_W ∧ mode ≠ MODE_RW, m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0

Rule argument

Additional information

Used simplifier rules: 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