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Proof step 2 from proof links-modmeta-write3 (previous step)

dirs[ino] = mkdir(m0, md0, n1, n2, entries), ino ∈ dirs ⊦ ino = ino2, ino = ino1, links(ino0, dirs[ino1, ad][ino2, ad0][ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs[ino1, ad][ino2, ad0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) ∧ ino ≠ ino1 → links(ino0, dirs[ino1, ad][ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs[ino1, ad])

Rule argument

spec: <toplevel> name: links-modmeta-write2 seq: ⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) ∧ ino ≠ ino1 → links (ino0, dirs[ino1, ad][ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs[ino1, ad]) subst: [m0, md0, n1, n2, entries, n0, n, md, m, ino, ad, ino1, dirs, ino0] → [m0, md0, n1, n2, entries, n0, n, md, m, ino, ad0, ino2, dirs[ino1, ad], ino0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s) Used terms: m0, md0, n1, n2, entries, n0, n, md, m, ino, ad0, ino2, dirs[ino1, ad], ino0