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Proof step 12 from proof valid-wl-map-indices (previous step)

apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0] = wl-entry(m1, stat), n0 < # wlar.mapIndices(nx, λ wle. wle.ec:= n), indices-erasing(wlar, nx), valid-indices(wlar, nx), ∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)) ⊦ dups(nx), (stat = erroneous ↔ boolvar) ∧ (stat = free → avhdr = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr = aechdr(m1)) ∧ (stat = used → (∃ v, m. valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, false)) ∧ avhdr.sqn = valid-sqns(v, m, apebs).max))

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [n0, λ wle. wle.ec:= n, nx, wlar] flags: <all paths>

Additional information

Used terms: n0, λ wle. wle.ec:= n, nx, wlar