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Proof step 14 from proof prepost-wl-get-used-min (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ n < # wlar → used-ecs(wlar, n + 1) = (wlar[n].status = used ⊃ used-ecs(wlar, n) ++ wlar[n].ec;used-ecs(wlar, n))
Proof step 16:
¬ boolvar ↔ used-ecs(wlar, m0) = ∅, wlar[vtblpnum] = wl-entry(m, stat), wlar[m0] = wl-entry(m1, used), m0 < # wlar, boolvar → vtblpnum < # wlar, boolvar → vtblpnum < m0 ∧ stat = used ∧ m = used-ecs(wlar, m0).min, ¬ boolvar ∨ m1 < m ⊦ m1 = (wlar[m0].status = used ⊃ used-ecs(wlar, m0) ++ wlar[m0].ec;used-ecs(wlar, m0)).min ∧ (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