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Proof step 14 from proof valid-eraseq-map-indices-nostatchange (previous step)

n ∈ q ↔ n < # wlar ∧ stat0 = erasing, wlar.mapIndices(nx, f)[n] = wl-entry(m, stat), wlar[n] = wl-entry(m0, stat0), valid-indices(wlar, nx), ∀ wle. f(wle).status = wle.status ⊦ n ∈ q ↔ n < # wlar ∧ stat = erasing, dups(nx)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ valid-indices(wlar, nx) ∧ ¬ dups(nx) ∧ n < # wlar → wlar.mapIndices(nx, f0)[n] = (n ∈ nx ⊃ f0(wlar[n]);wlar[n])
Proof step 16:
(n ∈ nx ⊃ f(wlar[n]);wlar[n]) = wl-entry(m, stat), n ∈ q ↔ n < # wlar ∧ stat0 = erasing, wlar[n] = wl-entry(m0, stat0), n < # wlar, valid-indices(wlar, nx), ∀ wle. f(wle).status = wle.status ⊦ n ∈ q ↔ n < # wlar ∧ stat = erasing, dups(nx)

Rule argument

spec: array-indices, inst: wlarray-base name: map-indices-at seq: ⊦ valid-indices(wlar, nx) ∧ ¬ dups(nx) ∧ n < # wlar → wlar.mapIndices(nx, f0)[n] = (n ∈ nx ⊃ f0(wlar[n]);wlar[n]) subst: [n, f0, nx, wlar] → [n, f, nx, wlar] flags: <all paths>

Additional information

Used terms: n, f, nx, wlar