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Proof step 4 from proof in-delta (previous step)

ecs(wlar).max = n0 + n1, wlar[n] = wl-entry(n0, stat), n < # wlar, sum-of-differences(n0 + n1, ecs(wlar)) < n1, n0 ∈ ecs(wlar) ⊦

User applied rule apply lemma

And obtained the following new goals

Proof step 5:
⊦ m ∈ bag → sum-of-differences(n, bag) ≥ n - m

Rule argument

spec: <toplevel> name: sum-of-differences-in seq: ⊦ m ∈ bag → sum-of-differences(n, bag) ≥ n - m subst: [m, bag, n] → [n0, ecs(wlar), n0 + n1]

Additional information

Used simplifier rules: in-ecs: ⊦ n < # wlar ∧ wlar[n] = wl-entry(m, stat) → m ∈ ecs(wlar);% ⊦ m + n - m = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: n0, ecs(wlar), n0 + n1