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Proof step 3 from proof delta-write (previous step)

n < # wlar, wlar[n].ec < ecs(wlar).max, m ≤ ecs(wlar).max ⊦ ecs(wlar).max + (sum-of-differences(ecs(wlar).max, ecs(wlar)) - (ecs(wlar).max - wlar[n].ec)) = m + sum-of-differences(ecs(wlar[n, wl-entry(m, stat)]).max, ecs(wlar[n, wl-entry(m, stat)]))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
ecs(wlar).max = n0 + wlar[n].ec, wlar[n].ec < ecs(wlar).max, n < # wlar, m ≤ ecs(wlar).max, wlar[n].ec ≤ ecs(wlar).max ⊦ ecs(wlar).max + (sum-of-differences(ecs(wlar).max, ecs(wlar)) - n0) = m + sum-of-differences(ecs(wlar[n, wl-entry(m, stat)]).max, ecs(wlar[n, wl-entry(m, stat)]))

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [ecs(wlar).max, wlar[n].ec, n0]

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: ecs(wlar).max, wlar[n].ec, n0