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Proof step 26 from proof delta-write (previous step)

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) -- m0), ecs(wlar) -- m0 = ∅, n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ sum-of-differences(n, bag -- m) = (m ∈ bag ⊃ sum-of-differences(n, bag) - (n - m);sum-of-differences(n, bag))
Proof step 28:
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

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), m] flags: <all paths>

Additional information

Used terms: m0, ecs(wlar), m