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Proof step 5 from proof in-ecs (previous step)

wlar[n] = wl-entry(m, stat), n < # wlar ⊦ m ∈ ecs(wlar, # wlar)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ n ≤ # wlar → (m ∈ ecs(wlar, n) ↔ (∃ n0. n0 < n ∧ wlar[n0].ec = m))
Proof step 7:
wlar[n] = wl-entry(m, stat), n < # wlar, # wlar ≤ # wlar ⊦ ∃ n0. n0 < # wlar ∧ wlar[n0].ec = m

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] → [# wlar, wlar, m] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < n; (s) Used terms: # wlar, wlar, m