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Proof step 9 from proof vols-is-max-is-min-eraseq (previous step)

# apebs = # wlar1, # wlar0 = # wlar1, apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar1), is-encoded(vtbl, buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, n0), valid-ebatbl(apebs, wlar1, vols1, m0), valid-eraseq(apebs, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-eraseq(apebs, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-strong(apebs, vtbl, q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), valid-vtbl(apebs, vols0, wlar0, n0), valid-vtbl(apebs, vols1, wlar1, m0), valid-wl(apebs, wlar0), valid-wl(apebs, wlar1), ∀ v. (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (∀ m. m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m])) ⊦ VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1, q0.lebrefs ⊆ q1.lebrefs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ s ⊆ s0 ↔ (∀ lref. lref ∈ s → lref ∈ s0)
Proof step 11:
# wlar0 = # wlar1, # apebs = # wlar1, apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), bflipset-cons(bflipset, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(vtbl, buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar1, vols1, m0), valid-ebatbl(apebs, wlar0, vols0, n0), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs, q1), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs, q0), valid-eraseq-strong(apebs, vtbl, q0), valid-global-sqn(apebs, m1), valid-global-sqn(apebs, n1), valid-vtbl(apebs, vols1, wlar1, m0), valid-vtbl(apebs, vols0, wlar0, n0), valid-wl(apebs, wlar1), valid-wl(apebs, wlar0), ∀ v. (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (∀ m. m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m])) ⊦ VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0, ∀ lref. lref ∈ q0.lebrefs → lref ∈ q1.lebrefs

Rule argument

spec: set-basic, inst: lebrefset name: Subset seq: ⊦ s ⊆ s0 ↔ (∀ lref. lref ∈ s → lref ∈ s0) subst: [s0, s] → [q1.lebrefs, q0.lebrefs] flags: <all paths>

Additional information

Used terms: q1.lebrefs, q0.lebrefs