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Proof step 97 from proof inv-truncate (previous step)

files0[m] = mkfile(m1, md1, # links(m, dirs), content0), files = files0[m, mkfile(m1, md1, # links(m, dirs), content0 upto min(n, m2))], inode = mkinode(m, md, false, # links(m, dirs), 0, m2), afs-cons(dirs, files0), m ∈ files0, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE ⊦ afs-cons(dirs, files), m2 ≤ n ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content0 ∨ buf-opt.some?)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 98:
files0[m] = mkfile(m1, md1, # links(m, dirs), content0), afs-cons(dirs, files0), m ∈ files0, ROOT_INO ∈ dirs, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE, 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 ∧ files0[ino].nlink = # links(ino, dirs), ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files0, ino ∈ files0 ∧ n0 ∈ files0[ino].content → # files0[ino].content[n0] = VFS_PAGE_SIZE ⊦ m2 ≤ n ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content0 ∨ buf-opt.some?), ( ino ∈ files0 → ¬ ino ∈ dirs ∧ (ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0 upto min(n, m2));files0[ino]).nlink = # links(ino, dirs)) ∧ ( ino ∈ files0 ∧ n0 ∈ (ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0 upto min(n, m2));files0[ino]).content → # (ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0 upto min(n, m2));files0[ino]).content[n0] = VFS_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: afs-cons-reduce: ⊦ afs-cons(dirs0, files0) → ( afs-cons(dirs1, files1) ↔ (∀ ino, name, n. ROOT_INO ∈ dirs0 ∧ ( ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dir-empty(ino, dirs0, files0)) ∧ ( ino ∈ dirs0 → ¬ ino ∈ files0 ∧ dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0)) ∧ ( ino ∈ files0 → ¬ ino ∈ dirs0 ∧ files0[ino].nlink = # links(ino, dirs0)) ∧ ( ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → valid-ino(dirs0[ino].entries[name], dirs0, files0)) ∧ ( ino ∈ files0 ∧ n ∈ files0[ino].content → valid-pagesize(ino, n, files0)) → ROOT_INO ∈ dirs1 ∧ ( ino ∈ dirs1 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs1) = ∅ → dir-empty(ino, dirs1, files1)) ∧ ( ino ∈ dirs1 → ¬ ino ∈ files1 ∧ dirs1[ino].nlink = # links(ino, dirs1) ∧ dirs1[ino].nlink ≤ 1 ∧ dirs1[ino].size = # dirs1[ino].entries ∧ dirs1[ino].nsubdirs = # subdirs(ino, dirs1)) ∧ ( ino ∈ files1 → ¬ ino ∈ dirs1 ∧ files1[ino].nlink = # links(ino, dirs1)) ∧ ( ino ∈ dirs1 ∧ name ∈ dirs1[ino].entries → valid-ino(dirs1[ino].entries[name], dirs1, files1)) ∧ ( ino ∈ files1 ∧ n ∈ files1[ino].content → valid-pagesize(ino, n, files1))));% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ afs-cons(dirs, files) → ROOT_INO ∈ dirs; (ss)%⊦ valid-pagesize(ino, n, files) ↔ # files[ino].content[n] = VFS_PAGE_SIZE; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (s)