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Proof step 28 from proof delta-write (previous step)

ecs(wlar).max = n0 + m0, wlar[n] = wl-entry(m0, stat0), n < # wlar, (ecs(wlar) -- m0).max ≤ n0 + m0, (ecs(wlar) -- m0).max ≤ m, m ≤ n0 + m0 ⊦ (n0 + m0) + (sum-of-differences(n0 + m0, ecs(wlar)) - n0) = m + (m0 ∈ ecs(wlar) ⊃ sum-of-differences(m, ecs(wlar)) - (m - m0);sum-of-differences(m, ecs(wlar))), ecs(wlar) -- m0 = ∅, n0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
ecs(wlar).max = n0 + m0, wlar[n] = wl-entry(m0, stat0), n < # wlar, m ≤ n0 + m0, (ecs(wlar) -- m0).max ≤ m, (ecs(wlar) -- m0).max ≤ n0 + m0 ⊦ (n0 + m0) + (sum-of-differences(n0 + m0, ecs(wlar)) - n0) = m + (sum-of-differences(m, ecs(wlar)) - (m - m0)), ecs(wlar) -- m0 = ∅, n0 = 0

Rule argument

Additional information

Used simplifier rules: in-ecs: ⊦ n < # wlar ∧ wlar[n] = wl-entry(m, stat) → m ∈ ecs(wlar);