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Proof step 16 from proof ecs-n-write (previous step)

wlar[n0] = wl-entry(m2, stat0), wlar[m] = wl-entry(m2, stat1), 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) ++ wlar[m, wl-entry(m0, stat)][n0].ec = ecs(wlar, n0) ++ m0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
wlar[m] = wl-entry(m2, stat1), wlar[n0] = wl-entry(m2, stat0), wlar[m, wl-entry(m0, stat)][n0] = wl-entry(m1, stat2), 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) ++ m1 = ecs(wlar, n0) ++ 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, wl-entry(m0, stat)][n0], m1, stat2]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[m, wl-entry(m0, stat)][n0], m1, stat2