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Proof step 30 from proof inv-write_inode (previous step)

dirs[m] = mkdir(m5, md1, m6, m7, entries), files[m] = mkfile(m3, md0, # links(m, dirs), content), files[ino] = mkfile(m0, md2, m1, content0), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ files, ino ∈ files ∧ n ∈ content0 → # content0[n] = VFS_PAGE_SIZE, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # 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 = ∅ ⊦ (ino ∈ files → ¬ ino ∈ dirs ∧ (ino = m ⊃ mkfile(m2, md, # links(m, dirs), content);files[ino]).nlink = # links(ino, dirs)) ∧ ( ino ∈ files ∧ n ∈ (ino = m ⊃ mkfile(m2, md, # links(m, dirs), content);files[ino]).content → # (ino = m ⊃ mkfile(m2, md, # links(m, dirs), content);files[ino]).content[n] = VFS_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
files[ino] = mkfile(m0, md2, m1, content0), files[m] = mkfile(m3, md0, # links(m, dirs), content), dirs[m] = mkdir(m5, md1, m6, m7, entries), afs-cons(dirs, files), m ∈ files, ROOT_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 ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files ⊦ ( ino ∈ files → ¬ ino ∈ dirs ∧ (ino = m ⊃ mkfile(m2, md, # links(m, dirs), content);mkfile(m0, md2, m1, content0)).nlink = # links(ino, dirs)) ∧ ( ino ∈ files ∧ n ∈ (ino = m ⊃ mkfile(m2, md, # links(m, dirs), content);mkfile(m0, md2, m1, content0)).content → # (ino = m ⊃ mkfile(m2, md, # links(m, dirs), content);mkfile(m0, md2, m1, content0)).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)