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Proof step 3 from proof links-deldir (previous step)

dirs[ino0] = mkdir(m, md, n, n0, ∅), ino0 ∈ dirs ⊦ links(ino, dirs -- ino0) = links(ino, dirs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0)

Rule argument

spec: set-basic, inst: alink-set name: Extension seq: ⊦ ls = ls0 ↔ (∀ alink. alink ∈ ls ↔ alink ∈ ls0) subst: [ls0, ls] → [links(ino, dirs), links(ino, dirs -- ino0)] flags: <all paths>

Additional information

Used simplifier rules: links: ⊦ alink ∈ links(ino, dirs) ↔ alink.pino ∈ dirs ∧ alink.name ∈ dirs[alink.pino].entries ∧ ino = dirs[alink.pino].entries[alink.name];% ⊦ ino ∈ dirs -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ dirs; (s)%ino ∈ dirs ⊦ ino ≠ ino0 → (dirs -- ino0)[ino] = dirs[ino]; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ ¬ str ∈ ∅; (s) Used terms: links(ino, dirs), links(ino, dirs -- ino0)