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Proof step 4 from proof delta-write (previous step)

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)]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
ecs(wlar).max = n0 + wlar[n].ec, wlar[n].ec < ecs(wlar).max, n < # wlar, m ≤ 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)])), n0 = 0

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → m ≤ n; (s)