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Proof step 31 from proof afs-cons-inode-sync (previous step)

dirs[ino] = mkdir(m5, md1, m6, m7, entries0), files[ino] = mkfile(m0, md0, # links(ino, dirs), content), afs-cons(dirs, files), ino ∈ files, m ∈ dirs, ROOT_INO ∈ dirs ⊦ # links(ino, dirs) = # links(ino, dirs[m, dirs[m].meta:= md]), ino ∈ dirs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ 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