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Proof step 23 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)) - ((ecs(wlar) -- m0).max - m0)), ecs(wlar) -- m0 = ∅, n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ 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: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ 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% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ m = m + n ↔ n = 0; (s) Used terms: m0, ecs(wlar)