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Proof step 25 from proof ecs-n-write (previous step)

wlar[m] = wl-entry(m2, stat1), wlar[n0] = wl-entry(m2, stat0), ecs(wlar[m, wl-entry(m0, stat)], n0) = (ecs(wlar, n0) -- m2) ++ m0, m < n0, m < # wlar, n0 < # wlar, m + 1 < # wlar ⊦ ecs(wlar, n0) ++ m2 = ecs(wlar, n0), n0 = m, m2 ∈ ecs(wlar, n0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ n ≤ # wlar → (m ∈ ecs(wlar, n) ↔ (∃ n0. n0 < n ∧ wlar[n0].ec = m))
Proof step 27:
wlar[n0] = wl-entry(m2, stat0), wlar[m] = wl-entry(m2, stat1), ecs(wlar[m, wl-entry(m0, stat)], n0) = (ecs(wlar, n0) -- m2) ++ m0, m + 1 < # wlar, n0 < # wlar, m < # wlar, m < n0, n0 ≤ # wlar ⊦ ecs(wlar, n0) ++ m2 = ecs(wlar, n0), n0 = m, ∃ n1. n1 < n0 ∧ wlar[n1].ec = m2

Rule argument

spec: <toplevel> name: in-ecs-n seq: ⊦ n ≤ # wlar → (m ∈ ecs(wlar, n) ↔ (∃ n0. n0 < n ∧ wlar[n0].ec = m)) subst: [n, wlar, m] → [n0, wlar, m2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s) Used terms: n0, wlar, m2