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Proof step 8 from proof afs-cons-reduce (previous step)

files0[ino] = mkfile(m, md, m0, content), files1[ino] = mkfile(m1, md0, m2, content0), afs-cons(dirs0, files0), afs-cons(dirs1, files1), ROOT_INO ∈ dirs0, ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → dirs0[ino].entries[name] ∈ dirs0 ∨ dirs0[ino].entries[name] ∈ files0, ino ∈ files0 → ¬ ino ∈ dirs0 ∧ m0 = # links(ino, dirs0), ino ∈ dirs0 → dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dirs0[ino].entries = ∅ ⊦ (ino ∈ dirs1 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs1) = ∅ → dirs1[ino].entries = ∅) ∧ ( ino ∈ dirs1 → 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 ∧ m2 = # links(ino, dirs1)) ∧ (ino ∈ dirs1 ∧ name ∈ dirs1[ino].entries → dirs1[ino].entries[name] ∈ dirs1 ∨ dirs1[ino].entries[name] ∈ files1) ∧ (ino ∈ files1 ∧ n ∈ content0 → # content0[n] = VFS_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
files1[ino] = mkfile(m1, md0, m2, content0), files0[ino] = mkfile(m, md, m0, content), afs-cons(dirs1, files1), afs-cons(dirs0, files0), ROOT_INO ∈ dirs0, ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dirs0[ino].entries = ∅, ino ∈ dirs0 → 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 ∧ m0 = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → dirs0[ino].entries[name] ∈ dirs0 ∨ dirs0[ino].entries[name] ∈ files0 ⊦ (ino ∈ dirs1 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs1) = ∅ → dirs1[ino].entries = ∅) ∧ ( ino ∈ dirs1 → 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 ∧ m2 = # links(ino, dirs1)) ∧ (ino ∈ dirs1 ∧ name ∈ dirs1[ino].entries → dirs1[ino].entries[name] ∈ dirs1 ∨ dirs1[ino].entries[name] ∈ files1)

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)