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Proof step 53 from proof vols-is-max-is-min-eraseq (previous step)

# apebs = # wlar1, # wlar0 = # wlar1, apebs[m0].vidhdr.leb = VTBL_LNUM, avhdr0.sqn = valid-sqns(v, m, apebs).max, wlar1[m0].status = used, apebs[m0].vidhdr.vol = VTBL_VOLID, wlar0[m0] = wl-entry(m3, erasing), apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar1[m0] = wl-entry(m5, used), apebs[m0] = mkpeb(aechdr(m5), avhdr0, buf0, m4, false), m0 < # apebs, m0 < # wlar1, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar1), is-encoded(to-vtbl(vols1), apebs[m0].data), is-encoded(vtbl, buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, n0), valid-eraseq(apebs, 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-peb(v, m, mkpeb(aechdr(m5), avhdr0, buf0, m4, false)), valid-vtbl(apebs, vols0, wlar0, n0), valid-wl(apebs, wlar0), eq-entry(m0, v × m) ∈ q0, m0 ∈ q0, ∀ 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])) ⊦ avhdr0 = empty, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1, v × m ∈ q1, vols1[v][m] = ⌜m0⌝ ∧ v ∈ vols1 ∧ m < # vols1[v], v ∈ vols0 ∧ m < # vols0[v]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
# wlar0 = # wlar1, # apebs = # wlar1, avhdr0.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, apebs[m0] = mkpeb(aechdr(m5), avhdr0, buf0, m4, false), wlar1[m0] = wl-entry(m5, used), apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar0[m0] = wl-entry(m3, erasing), m0 < # wlar1, bflipset-cons(bflipset, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(to-vtbl(vols1), buf0), is-encoded(vtbl, buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, n0), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs, q1), valid-eraseq(q0), valid-eraseq(apebs, q0), valid-eraseq-strong(apebs, vtbl, q0), valid-global-sqn(apebs, m1), valid-global-sqn(apebs, n1), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m5), avhdr0, buf0, m4, false)), valid-vtbl(apebs, vols0, wlar0, n0), valid-wl(apebs, wlar0), m0 ∈ q0, eq-entry(m0, VTBL_VOLID × VTBL_LNUM) ∈ q0, ∀ 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])) ⊦ avhdr0 = empty, VTBL_VOLID × VTBL_LNUM ∈ q1, VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ v ∈ vols → vols[v] = (∅)[v]; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.vol = v; (s)% ⊦ wl-entry(m, stat).status = stat; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.leb = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)