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Proof step 15 from proof prepost-get-pebs-for-wl (previous step)

# apebs = # wlar, ¬ boolvar ↔ free-ecs(wlar) = ∅, boolvar0 ↔ false, bflipset0 = bflipset, boolvar, bflipset-cons(bflipset, 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), boolvar → n = free-ecs(wlar).min ⊦ ⟪ubi_wl_find_free_max_below#(n + 2 * WL_THRESHOLD, wlar; vtblpnum0); if bflipset ≠ ∅ then choose n with n ∈ bflipset in {vtblpnum := n; bflipset := bflipset -- n; boolvar0 := true} else {ubi_wl_get_used_min#(wlar; vtblpnum; boolvar); if boolvar ∧ wlar[vtblpnum].ec + WL_THRESHOLD ≤ wlar[vtblpnum0].ec then boolvar0 := true}⟫ ( bflipset-cons(bflipset, wlar) ∧ ( boolvar0 → vtblpnum0 < # wlar ∧ wlar[vtblpnum0].status = free ∧ vtblpnum < # wlar ∧ wlar[vtblpnum].status = used ∧ (bflipset0 = ∅ → wlar[vtblpnum].ec + WL_THRESHOLD ≤ wlar[vtblpnum0].ec))), VTBL_VOLID ∈ vols, vtblpnum1 ∈ q

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
# apebs = # wlar, # free-ecs(wlar) ≠ 0, free-ecs(wlar) ≠ ∅, bflipset-cons(bflipset, 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_find_free_max_below#(free-ecs(wlar).min + 2 * WL_THRESHOLD, wlar; vtblpnum0); bflipset0 := bflipset; boolvar0 := false; if bflipset ≠ ∅ then choose n with n ∈ bflipset in {vtblpnum := n; bflipset := bflipset -- n; boolvar0 := true} else {ubi_wl_get_used_min#(wlar; vtblpnum; boolvar); if boolvar ∧ wlar[vtblpnum].ec + WL_THRESHOLD ≤ wlar[vtblpnum0].ec then boolvar0 := true}⟫ ( bflipset-cons(bflipset, wlar) ∧ ( boolvar0 → vtblpnum0 < # wlar ∧ wlar[vtblpnum0].status = free ∧ vtblpnum < # wlar ∧ wlar[vtblpnum].status = used ∧ (bflipset0 = ∅ → wlar[vtblpnum].ec + WL_THRESHOLD ≤ wlar[vtblpnum0].ec)))

Rule argument

Additional information

Used simplifier rules: size-zero: ⊦ # ns ≠ 0 → ns ≠ ∅; (forward) from specification set-basic[nat-set]%size-zero-01: ⊦ ns ≠ ∅ → # ns ≠ 0; (forward) from specification set-basic[nat-set]