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Proof step 10 from proof ecs-n-write (previous step)

wlar[n0] = wl-entry(m1, stat0), m < # wlar, n0 < # wlar, m ≤ n0, ∀ wlar, m, wle. n0 ≤ # wlar → ecs(wlar[m, wle], n0) = (m < n0 ⊃ (ecs(wlar, n0) -- wlar[m].ec) ++ wle.ec;ecs(wlar, n0)) ⊦ ecs(wlar[m, wl-entry(m0, stat)], n0 + 1) = (m1 = wlar[m].ec ⊃ ecs(wlar, n0);(ecs(wlar, n0) -- wlar[m].ec) ++ m1) ++ m0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
wlar[n0] = wl-entry(m1, stat0), wlar[m] = wl-entry(m2, stat1), n0 < # wlar, m < # wlar, m ≤ n0, ∀ wlar, m, wle. n0 ≤ # wlar → ecs(wlar[m, wle], n0) = (m < n0 ⊃ (ecs(wlar, n0) -- wlar[m].ec) ++ wle.ec;ecs(wlar, n0)) ⊦ ecs(wlar[m, wl-entry(m0, stat)], n0 + 1) = (m1 = m2 ⊃ ecs(wlar, n0);(ecs(wlar, n0) -- m2) ++ m1) ++ m0

Rule argument

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [wlar[m], m2, stat1]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[m], m2, stat1