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Proof step 29 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)) - (m - m0)), ecs(wlar) -- m0 = ∅, n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ m ≠ bag.max → (bag -- m).max = bag.max

Rule argument

spec: bag-max name: bag-rem-notmax seq: ⊦ m ≠ bag.max → (bag -- m).max = bag.max subst: [m, bag] → [m0, ecs(wlar)] flags: <all paths>

Additional information

Used simplifier rules: let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m = m + n ↔ n = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m; (s)% ⊦ m + n - m = n; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s) Used terms: m0, ecs(wlar)