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Proof step 5 from proof valid-eraseq-map-indices-nostatchange (previous step)

valid-indices(wlar, nx), ∀ wle. f(wle).status = wle.status, ∀ n. n ∈ q ↔ n < # wlar ∧ wlar[n].status = erasing ⊦ dups(nx), valid-eraseq(wlar.mapIndices(nx, f), q)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ valid-eraseq(wlar, q) ↔ (∀ n. n ∈ q ↔ n < # wlar ∧ wlar[n].status = erasing)
Proof step 7:
valid-indices(wlar, nx), ∀ n. n ∈ q ↔ n < # wlar ∧ wlar[n].status = erasing, ∀ wle. f(wle).status = wle.status ⊦ dups(nx), ∀ n. n ∈ q ↔ n < # wlar.mapIndices(nx, f) ∧ wlar.mapIndices(nx, f)[n].status = erasing

Rule argument

spec: ubi-base name: valid-eraseqw seq: ⊦ valid-eraseq(wlar, q) ↔ (∀ n. n ∈ q ↔ n < # wlar ∧ wlar[n].status = erasing) subst: [q, wlar] → [q, wlar.mapIndices(nx, f)] flags: <all paths>

Additional information

Used terms: q, wlar.mapIndices(nx, f)