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Proof step 6 from proof lastlink-move (previous step)

dirs[ino1] = mkdir(m1, md1, n1, n3, entries1), dirs[ino0] = mkdir(m0, md0, n0, n2, entries0), links(entries0[str0], dirs) = ∅ ++ alink, str1 ∈ entries1, str0 ∈ entries0, ino1 ∈ dirs, ino0 ∈ dirs ⊦ entries0[str0] = entries1[str1] ↔ str0 = str1 ∧ ino0 = ino1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0)
Proof step 8:
dirs[ino0] = mkdir(m0, md0, n0, n2, entries0), dirs[ino1] = mkdir(m1, md1, n1, n3, entries1), ino0 ∈ dirs, ino1 ∈ dirs, str0 ∈ entries0, str1 ∈ entries1, ∀ alink0. alink0 ∈ links(entries0[str0], dirs) ↔ alink0 ∈ ∅ ++ alink ⊦ entries0[str0] = entries1[str1] ↔ str0 = str1 ∧ ino0 = ino1

Rule argument

spec: set-basic, inst: alink-set name: Extension seq: ⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0) subst: [ls0, ls] → [∅ ++ alink, links(entries0[str0], dirs)] flags: <all paths>

Additional information

Used terms: ∅ ++ alink, links(entries0[str0], dirs)