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Proof step 14 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 + (m - m) + sum-of-differences((ecs(wlar) -- m0 = ∅ ⊃ m;(m < (ecs(wlar) -- m0).max ⊃ (ecs(wlar) -- m0).max;m)), ecs(wlar) -- m0), n0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
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

Rule argument

Additional information

Used simplifier rules: sum-of-differences-base: ⊦ sum-of-differences(n, ∅) = 0;%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ m - m = 0; (s)