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Proof step 7 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(ecs(wlar[n, wl-entry(m, stat)]).max, ecs(wlar[n, wl-entry(m, stat)])), n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ecs(wlar[m, wle]) = (m < # wlar ⊃ (ecs(wlar) -- wlar[m].ec) ++ wle.ec;ecs(wlar))
Proof step 9:
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

Rule argument

spec: <toplevel> name: ecs-write seq: ⊦ ecs(wlar[m, wle]) = (m < # wlar ⊃ (ecs(wlar) -- wlar[m].ec) ++ wle.ec ;ecs(wlar) ) subst: [wle, m, wlar] → [wl-entry(m, stat), n, wlar] flags: <all paths>

Additional information

Used terms: wl-entry(m, stat), n, wlar