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Proof step 7 from proof inv-erase-all (previous step)

# apebs1 = # wlar0, # apebs = # wlar, q1 ≠ [], bflipset-cons(bflipset, wlar0), bflipset-cons(bflipset, wlar), id(apebs, apebs1, mapped-pebs(vols)), ubi-io-inv(apebs), ubi-io-inv(apebs1), unique-sqns(apebs1), unique-sqns(apebs), valid-ebatbl(apebs1, wlar0, vols, vtblpnum), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-eraseq(q2), valid-eraseq(wlar0, q2), valid-eraseq(apebs1, q2), valid-eraseq(q1), valid-eraseq(wlar, q1), valid-eraseq(apebs, q1), valid-global-sqn(apebs1, sqnum), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs1, vols, wlar0, vtblpnum), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs1, wlar0), valid-wl(apebs, wlar), q1 ⊆ q2, ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum ∈ q1, ¬ vtblpnum ∈ q2 ⊦ ⟪ubi_erase_worker_helper#(q1.head.pnum; wlar, apebs; err); q := q1; if err = ESUCCESS then q := q.tail⟫ ( # 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, vtblpnum) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum) ∧ ubi-io-inv(apebs) ∧ id(apebs, apebs1, mapped-pebs(vols)) ∧ q ⊆ q2 ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS ⊃ # q;0) < # q1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
# apebs = # wlar, # apebs1 = # wlar0, q1 = eqent + q0, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), id(apebs, apebs1, mapped-pebs(vols)), ubi-io-inv(apebs1), ubi-io-inv(apebs), unique-sqns(apebs), unique-sqns(apebs1), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-ebatbl(apebs1, wlar0, vols, vtblpnum), valid-eraseq(apebs, q1), valid-eraseq(wlar, q1), valid-eraseq(q1), valid-eraseq(apebs1, q2), valid-eraseq(wlar0, q2), valid-eraseq(q2), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs1, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-vtbl(apebs1, vols, wlar0, vtblpnum), valid-wl(apebs, wlar), valid-wl(apebs1, wlar0), q1 ⊆ q2 ⊦ ⟪ubi_erase_worker_helper#(eqent.pnum; wlar, apebs; err); q := q1; if err = ESUCCESS then q := q.tail⟫ ( # 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, vtblpnum) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum) ∧ ubi-io-inv(apebs) ∧ id(apebs, apebs1, mapped-pebs(vols)) ∧ q ⊆ q2 ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS ⊃ # q;0) < # q1), q1 = [], VTBL_VOLID ∈ vols, vtblpnum ∈ q1, vtblpnum ∈ q2

Rule argument

spec: list-data, inst: erasequeue-base name: elim-list-c seq: q ≠ [] ⊦ eqent = q.head ∧ q0 = q.tail ↔ q = eqent + q0 subst: [q, eqent, q0] → [q1, eqent, q0]

Additional information

Used simplifier rules: q ≠ [] ⊦ eqent = q.head ∧ q0 = q.tail ↔ q = eqent + q0; (elim) Used terms: q1, eqent, q0