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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
n0 < # wlar.mapIndices(nx, λ wle. wle.ec:= n), indices-erasing(wlar, nx), valid-indices(wlar, nx), valid-wl(apebs, wlar) ⊦ dups(nx), (wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0].status = erroneous ↔ apebs[n0].bad) ∧ (wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0].status = free → apebs[n0].vidhdr = empty) ∧ ( wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0].status ≠ erroneous ∧ wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0].status ≠ erasing → apebs[n0].echdr = aechdr(wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0].ec)) ∧ ( wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0].status = used → (∃ v, m. valid-peb(v, m, apebs[n0]) ∧ apebs[n0].vidhdr.sqn = valid-sqns(v, m, apebs).max))

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic