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Proof step 15 from proof delta-write (previous step)

ecs(wlar) -- m0 = ∅, 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, n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: bag-rem-eq-empty-elim seq: ⊦ bag -- m = ∅ ↔ bag = ∅ ∨ bag = ∅ ++ m subst: [m, bag] → [m0, ecs(wlar)] flags: <all paths>

Additional information

Used simplifier rules: ecs-empty: ⊦ ecs(wlar) = ∅ ↔ # wlar = 0;%sum-of-differences-rec: ⊦ sum-of-differences(n, bag ++ m) = (n - m) + sum-of-differences(n, bag);%sum-of-differences-base: ⊦ sum-of-differences(n, ∅) = 0;% ⊦ m < n → n ≠ 0; (s)% ⊦ 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 + 0 = n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < n; (s)%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ (∅ ++ n).max = n; (s)% ⊦ m = m + n ↔ n = 0; (s) Used terms: m0, ecs(wlar)