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Proof step 20 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, wlar[m].status = used → boolvar → m < # wlar ∧ vtblpnum < # wlar, boolvar → vtblpnum < m ∧ wlar[vtblpnum].status = used ∧ wlar[vtblpnum].ec = used-ecs(wlar, m).min ⊦ wlar[m].status = used ∧ (¬ boolvar ∨ wlar[m].ec < wlar[vtblpnum].ec), ( m + 1 ≤ # wlar ∧ (boolvar → vtblpnum < m + 1 ∧ wlar[vtblpnum].status = used ∧ wlar[vtblpnum].ec = used-ecs(wlar, m + 1).min) ∧ (¬ boolvar ↔ used-ecs(wlar, m + 1) = ∅)) ∧ # wlar - m + 1 < # wlar - m0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
¬ boolvar ↔ used-ecs(wlar, m0) = ∅, m0 < # wlar, wlar[m0].status = used → boolvar → vtblpnum < # wlar, boolvar → vtblpnum < m0 ∧ wlar[vtblpnum].status = used ∧ wlar[vtblpnum].ec = used-ecs(wlar, m0).min ⊦ (boolvar → ¬ m0 < vtblpnum ∧ wlar[vtblpnum].status = used ∧ wlar[vtblpnum].ec = used-ecs(wlar, m0 + 1).min) ∧ (¬ boolvar ↔ used-ecs(wlar, m0 + 1) = ∅), wlar[m0].status = used ∧ (¬ boolvar ∨ wlar[m0].ec < wlar[vtblpnum].ec)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ ¬ n < n; (s)% ⊦ n < m → (m - n) + n = m; (s)%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n + 1 ↔ ¬ n < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m < n → m ≤ n; (s)