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Proof step 88 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), files1[ino] = mkfile(m2, md0, m3, content), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files1), of-cons (of, dirs, files1[m, mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1)]), of-cons(of, dirs, files1), m ∈ files1, m1 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, ROOT_INO ∈ dirs, n0 ≤ # buf0, n2 + n1 ≤ VFS_PAGE_SIZE, ino ∈ files1 ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files1, ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, ino ∈ files1 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs) ⊦ n0 = 0, n2 = 0, ( ino ∈ files1 → ¬ ino ∈ dirs ∧ (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1) ;files1[ino] ) .nlink = # links(ino, dirs)) ∧ ( ino ∈ files1 ∧ n ∈ (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1) ;files1[ino] ) .content → # (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1) ;files1[ino] ) .content [n ] = VFS_PAGE_SIZE), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 89:
m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files1[ino] = mkfile(m2, md0, m3, content), files1[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files1), of-cons(of, dirs, files1), of-cons (of, dirs, files1[m, mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1)]), ROOT_INO ∈ dirs, fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n2 + n1 ≤ VFS_PAGE_SIZE, n0 ≤ # buf0, ino ∈ files1 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files1 ⊦ n0 = 0, n2 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, ( ino ∈ files1 → ¬ ino ∈ dirs ∧ (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1) ;mkfile(m2, md0, m3, content) ) .nlink = # links(ino, dirs)) ∧ ( ino ∈ files1 ∧ n ∈ (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1) ;mkfile(m2, md0, m3, content) ) .content → # (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1) ;mkfile(m2, md0, m3, content) ) .content [n ] = VFS_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)