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Proof step 20 from proof delta-write (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ sum-of-differences(n, bag -- m) = (m ∈ bag ⊃ sum-of-differences(n, bag) - (n - m);sum-of-differences(n, bag))
Proof step 22:
ecs(wlar).max = n0 + m0, wlar[n] = wl-entry(m0, stat0), m < (ecs(wlar) -- m0).max, n < # wlar, m ≤ n0 + m0 ⊦ (n0 + m0) + (sum-of-differences(n0 + m0, ecs(wlar)) - n0) = (ecs(wlar) -- m0).max + (m0 ∈ ecs(wlar) ⊃ sum-of-differences((ecs(wlar) -- m0).max, ecs(wlar)) - ((ecs(wlar) -- m0).max - m0) ;sum-of-differences((ecs(wlar) -- m0).max, ecs(wlar)) ), ecs(wlar) -- m0 = ∅, n0 = 0

Rule argument

spec: <toplevel> name: sum-of-differences-rem seq: ⊦ sum-of-differences(n, bag -- m) = (m ∈ bag ⊃ sum-of-differences(n, bag) - (n - m) ;sum-of-differences(n, bag) ) subst: [m, bag, n] → [m0, ecs(wlar), (ecs(wlar) -- m0).max] flags: <all paths>

Additional information

Used terms: m0, ecs(wlar), (ecs(wlar) -- m0).max