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Proof step 6 from proof prepost-get-peb (previous step)

# apebs = # wlar, bflipset-cons(bflipset, wlar), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum0), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum0), valid-wl(apebs, wlar), ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum0 ∈ q ⊦ ⟪ubi_wl_get_free_min#(wlar; n; boolvar); wlar0 := wlar; q0 := q; apebs0 := apebs; if ¬ boolvar then if q ≠ [] then {vtblpnum := q.head.pnum; ubi_erase_worker_helper#(vtblpnum; wlar, apebs; err); if err = ESUCCESS then {q := q.tail; if wlar[vtblpnum].status ≠ free then err := ENOSPC} else err := ENOSPC} else err := ENOSPC else {ubi_wl_find_free_max_below#(n + WL_THRESHOLD, wlar; vtblpnum); err := ESUCCESS}⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err ≠ ESUCCESS → # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum0) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum0)) ∧ ubi-io-inv(apebs) ∧ q.lebrefs ⊆ q0.lebrefs ∧ id(apebs, apebs0, mapped-pebs(vols)) ∧ ( err = ESUCCESS → vtblpnum < # apebs ∧ wlar[vtblpnum].status = free ∧ ( apebs0 = apebs ∧ wlar0 = wlar ∧ q0 = q ∨ id○(apebs0, apebs, vtblpnum) ∧ id○(wlar0, wlar, vtblpnum) ∧ q0 ≠ [] ∧ q0 = eq-entry(vtblpnum, q0.head.lebref) ' + q) ∧ # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum0) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum0)))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: prepost-wl-get-free-min seq: ⊦ ⟪ubi_wl_get_free_min#(wlar; n; boolvar)⟫ ( (boolvar → n = free-ecs(wlar).min) ∧ (¬ boolvar ↔ free-ecs(wlar) = ∅)) subst: [wlar, n, boolvar] → [wlar, n, boolvar] flags: <all paths>

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