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Proof step 36 from proof afs-cons-inode-sync (previous step)

files[ino] = mkfile(m0, md0, m1, content), dirs[ino] = mkdir(# entries0, md1, # links(ino, dirs), # subdirs(ino, dirs), entries0), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ dirs, # links(ino, dirs) ≤ 1, ino ∈ dirs ∧ name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries0 = ∅ ⊦ # links(ino, dirs) = # links(ino, dirs[m, dirs[m].meta:= md]), ino = m, ¬ ino ∈ dirs ∧ (ino ∈ files → m1 = # links(ino, dirs[m, dirs[m].meta:= md]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ m ∈ dirs → links(ino, dirs[m, dirs[m].meta:= md]) = links(ino, dirs)

Rule argument

spec: afs-base name: link-mod-dir-meta seq: ⊦ m ∈ dirs → links(ino, dirs[m, dirs[m].meta:= md]) = links(ino, dirs) subst: [md, m, dirs, ino] → [md, m, dirs, ino] flags: <all paths>

Additional information

Used terms: md, m, dirs, ino