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Proof step 30 from proof afs-cons-reduce (previous step)

files0[ino] = mkfile(m4, md1, m5, content0), files1[ino] = mkfile(m, md, m0, content), dirs1[ino] = mkdir(m1, md0, m2, m3, entries), afs-cons(dirs0, files0) ⊦ ROOT_INO ∈ dirs1 ∧ (ino ∈ dirs1 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs1) = ∅ → entries = ∅) ∧ (ino ∈ dirs1 → ¬ ino ∈ files1 ∧ m2 = # links(ino, dirs1) ∧ # links(ino, dirs1) ≤ 1 ∧ m1 = # entries ∧ m3 = # subdirs(ino, dirs1)) ∧ (ino ∈ files1 → ¬ ino ∈ dirs1 ∧ m0 = # links(ino, dirs1)) ∧ (ino ∈ dirs1 ∧ name ∈ entries → entries[name] ∈ dirs1 ∨ entries[name] ∈ files1) ∧ (ino ∈ files1 ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE), (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 ∧ m5 = # links(ino, dirs0)) ∧ (ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → dirs0[ino].entries[name] ∈ dirs0 ∨ dirs0[ino].entries[name] ∈ files0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 31:
dirs1[ino] = mkdir(m1, md0, m2, m3, entries), files1[ino] = mkfile(m, md, m0, content), files0[ino] = mkfile(m4, md1, m5, content0), dirs0[ino] = mkdir(m6, md2, m7, m8, entries0), afs-cons(dirs0, files0) ⊦ (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries0 = ∅) ∧ (ino ∈ dirs0 → m7 = # links(ino, dirs0) ∧ m7 ≤ 1 ∧ m6 = # entries0 ∧ m8 = # subdirs(ino, dirs0)) ∧ (ino ∈ files0 → ¬ ino ∈ dirs0 ∧ m5 = # links(ino, dirs0)) ∧ (ino ∈ dirs0 ∧ name ∈ entries0 → entries0[name] ∈ dirs0 ∨ entries0[name] ∈ files0), ROOT_INO ∈ dirs1 ∧ (ino ∈ dirs1 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs1) = ∅ → entries = ∅) ∧ (ino ∈ dirs1 → ¬ ino ∈ files1 ∧ m2 = # links(ino, dirs1) ∧ # links(ino, dirs1) ≤ 1 ∧ m1 = # entries ∧ m3 = # subdirs(ino, dirs1)) ∧ (ino ∈ files1 → ¬ ino ∈ dirs1 ∧ m0 = # links(ino, dirs1)) ∧ (ino ∈ dirs1 ∧ name ∈ entries → entries[name] ∈ dirs1 ∨ entries[name] ∈ files1) ∧ (ino ∈ files1 ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE)

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs0[ino], m6, md2, m7, m8, entries0]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs0[ino], m6, md2, m7, m8, entries0