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Proof step 32 from proof prepost-wl-get-used-min (previous step)

¬ boolvar ↔ used-ecs(wlar, m) = ∅, boolvar0 ↔ false, m = m0, m1 = 0, vtblpnum0 = n, m < # wlar, m ≤ # wlar, boolvar → vtblpnum < m ∧ wlar[vtblpnum].status = used ∧ wlar[vtblpnum].ec = used-ecs(wlar, m).min ⊦ m < # wlar ∧ (wlar[m].status = used → boolvar → m < # wlar ∧ vtblpnum < # wlar)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%size-zero-01: ⊦ ns ≠ ∅ → # ns ≠ 0; (forward) from specification set-basic[nat-set]%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%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 ↔ ¬ n ≤ m; (ss)% ⊦ m < n → m ≤ n; (s)