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Proof step 53 from proof prepost-get-pebs-for-wl (previous step)

# apebs = # wlar, wlar[vtblpnum0].ec = below(free-ecs(wlar), free-ecs(wlar).min + 2 * WL_THRESHOLD).max, wlar[vtblpnum0].status = free, wlar[m] = wl-entry(m0, free), # free-ecs(wlar) ≠ 0, free-ecs(wlar) ≠ ∅, vtblpnum1 ≠ m, m < # wlar, m0 < free-ecs(wlar).min + 2 * WL_THRESHOLD, vtblpnum0 < # wlar, unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum1), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum1), valid-wl(apebs, wlar), ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum1 ∈ q ⊦ ⟪ubi_wl_get_used_min#(wlar; vtblpnum; boolvar); boolvar0 := false; if boolvar ∧ wlar[vtblpnum].ec + WL_THRESHOLD ≤ wlar[vtblpnum0].ec then boolvar0 := true⟫ (boolvar0 → vtblpnum < # wlar ∧ wlar[vtblpnum].status = used ∧ wlar[vtblpnum].ec + WL_THRESHOLD ≤ wlar[vtblpnum0].ec)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 54:
# apebs = # wlar, wlar[m] = wl-entry(m0, free), wlar[vtblpnum0] = wl-entry(m1, stat), m1 = below(free-ecs(wlar), free-ecs(wlar).min + 2 * WL_THRESHOLD).max, stat = free, vtblpnum0 < # wlar, m0 < free-ecs(wlar).min + 2 * WL_THRESHOLD, m < # wlar, unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum1), valid-wl(apebs, wlar) ⊦ ⟪ubi_wl_get_used_min#(wlar; vtblpnum; boolvar); boolvar0 := false; if boolvar ∧ wlar[vtblpnum].ec + WL_THRESHOLD ≤ m1 then boolvar0 := true⟫ (boolvar0 → vtblpnum < # wlar ∧ wlar[vtblpnum].status = used ∧ wlar[vtblpnum].ec + WL_THRESHOLD ≤ m1), # free-ecs(wlar) = 0, free-ecs(wlar) = ∅, vtblpnum1 = m, VTBL_VOLID ∈ vols, vtblpnum1 ∈ q

Rule argument

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [wlar[vtblpnum0], m1, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[vtblpnum0], m1, stat