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Proof step 23 from proof prepost-wl-get-used-min (previous step)

¬ boolvar ↔ used-ecs(wlar, m0) = ∅, wlar[m0] = wl-entry(m, stat), wlar[vtblpnum] = wl-entry(m1, stat0), m0 < # wlar, stat = used → boolvar → vtblpnum < # wlar, boolvar → vtblpnum < m0 ∧ stat0 = used ∧ m1 = used-ecs(wlar, m0).min ⊦ (boolvar → ¬ m0 < vtblpnum ∧ stat0 = used ∧ m1 = used-ecs(wlar, m0 + 1).min) ∧ (¬ boolvar ↔ used-ecs(wlar, m0 + 1) = ∅), stat = used ∧ (¬ boolvar ∨ m < m1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ n < # wlar → used-ecs(wlar, n + 1) = (wlar[n].status = used ⊃ used-ecs(wlar, n) ++ wlar[n].ec;used-ecs(wlar, n))
Proof step 25:
¬ boolvar ↔ used-ecs(wlar, m0) = ∅, wlar[vtblpnum] = wl-entry(m1, stat0), wlar[m0] = wl-entry(m, stat), m0 < # wlar, boolvar → vtblpnum < m0 ∧ stat0 = used ∧ m1 = used-ecs(wlar, m0).min, stat = used → boolvar → vtblpnum < # wlar ⊦ stat = used ∧ (¬ boolvar ∨ m < m1), (boolvar → ¬ m0 < vtblpnum ∧ stat0 = used ∧ m1 = (wlar[m0].status = used ⊃ used-ecs(wlar, m0) ++ wlar[m0].ec;used-ecs(wlar, m0)).min) ∧ (¬ boolvar ↔ (wlar[m0].status = used ⊃ used-ecs(wlar, m0) ++ wlar[m0].ec;used-ecs(wlar, m0)) = ∅)

Rule argument

spec: wlarray name: used-ecs-rec seq: ⊦ n < # wlar → used-ecs(wlar, n + 1) = (wlar[n].status = used ⊃ used-ecs(wlar, n) ++ wlar[n].ec ;used-ecs(wlar, n) ) subst: [n, wlar] → [m0, wlar] flags: <all paths>

Additional information

Used terms: m0, wlar