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Proof step 9 from proof delta-write (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
ecs(wlar).max = n0 + m0, wlar[n] = wl-entry(m0, stat0), n < # wlar, m ≤ n0 + m0 ⊦ (n0 + m0) + (sum-of-differences(n0 + m0, ecs(wlar)) - n0) = m + (((ecs(wlar) -- m0) ++ m).max - m) + sum-of-differences(((ecs(wlar) -- m0) ++ m).max, ecs(wlar) -- m0), n0 = 0

Rule argument

Additional information

Used simplifier rules: sum-of-differences-rec: ⊦ sum-of-differences(n, bag ++ m) = (n - m) + sum-of-differences(n, bag);%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ wl-entry(m, stat).ec = m; (s)