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Proof step 34 from proof inv-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m] = mkfile(m1, md1, # links(m, dirs), content0), files0[ino] = mkfile(m0, md, m3, content), buf-opt.some?, afs-cons(dirs, files0), ROOT_INO ∈ dirs, m ∈ files0, m2 ≤ n, ino ∈ files0 ∧ n1 ∈ content → # content[n1] = VFS_PAGE_SIZE, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files0, ino ∈ files0 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs), 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 = ∅ ⊦ m2 % VFS_PAGE_SIZE = 0, ( ino ∈ files0 → ¬ ino ∈ dirs ∧ (ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .nlink = # links(ino, dirs)) ∧ ( ino ∈ files0 ∧ n1 ∈ (ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .content → # (ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .content [n1 ] = VFS_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[ino] = mkfile(m0, md, m3, content), files0[m] = mkfile(m1, md1, # links(m, dirs), content0), buf-opt.some?, afs-cons(dirs, files0), m ∈ files0, ROOT_INO ∈ dirs, m2 ≤ n, 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 ∈ files0 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs), ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files0 ⊦ m2 % VFS_PAGE_SIZE = 0, ( ino ∈ files0 → ¬ ino ∈ dirs ∧ (ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m0, md, m3, content) ) .nlink = # links(ino, dirs)) ∧ ( ino ∈ files0 ∧ n1 ∈ (ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m0, md, m3, content) ) .content → # (ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m0, md, m3, content) ) .content [n1 ] = 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)