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Proof step 11 from proof in-ecs-n (previous step)

wlar[n0] = wl-entry(m0, stat), n0 < # wlar, m ∈ ecs(wlar, n0), n0 ≤ # wlar → (m ∈ ecs(wlar, n0) ↔ (∃ n1. n1 < n0 ∧ wlar[n1].ec = m)) ⊦ ∃ n. ¬ n0 < n ∧ wlar[n].ec = m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
wlar[n0] = wl-entry(m0, stat), n < # wlar, n < n0, n0 < # wlar, n + 1 < # wlar, wlar[n].ec ∈ ecs(wlar, n0) ⊦ ∃ n1. ¬ n0 < n1 ∧ wlar[n1].ec = wlar[n].ec

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → m ≤ n; (s)