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Proof step 372 from proof inv-write (previous step)

of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m1, md, # links(m, dirs), content0), files0[ino] = mkfile(m2, md0, m3, content), dom of < ino3, afs-cons(dirs, files0), of-cons(of, dirs, files0[m, mkfile(m1, md, # links(m, dirs), content0 upto m1)]), of-cons(of, dirs, files0), m ∈ files0, fd ∈ of, ROOT_INO ∈ dirs, n0 ≤ # buf0, ino ∈ files0 ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files0, 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 ∈ files0 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs) ⊦ n0 = 0, (ino ∈ files0 → ¬ ino ∈ dirs ∧ (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0 upto m1);files0[ino]).nlink = # links(ino, dirs)) ∧ ( ino ∈ files0 ∧ n ∈ (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0 upto m1);files0[ino]).content → # (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0 upto m1);files0[ino]).content[n] = VFS_PAGE_SIZE), m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 373:
files0[ino] = mkfile(m2, md0, m3, content), files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), dom of < ino3, afs-cons(dirs, files0), of-cons(of, dirs, files0), of-cons(of, dirs, files0[m, mkfile(m1, md, # links(m, dirs), content0 upto m1)]), ROOT_INO ∈ dirs, fd ∈ of, m ∈ files0, n0 ≤ # buf0, ino ∈ files0 → ¬ 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] ∈ files0 ⊦ n0 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, ( ino ∈ files0 → ¬ ino ∈ dirs ∧ (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0 upto m1);mkfile(m2, md0, m3, content)).nlink = # links(ino, dirs)) ∧ ( ino ∈ files0 ∧ n ∈ (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0 upto m1);mkfile(m2, md0, m3, content)).content → # (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0 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)