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Proof step 85 from proof vols-is-max-is-max-vols (previous step)

# wlar0 = # wlar1, # apebs = # wlar1, # vols0[v] = # vols1[v], avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, wlar0[m6] = wl-entry(m16, used), apebs[m6] = mkpeb(aechdr(m16), avidhdr(v, m, valid-sqns(v1, m17, apebs).max, m13, m14), buf1, m15, false), wlar1[m5] = wl-entry(m10, used), apebs[m5] = mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false), wlar1[m0] = wl-entry(m4, used), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar0[m0] = wl-entry(m3, used), ⌜m6⌝ = vols0[v][m], ⌜m5⌝ = vols1[v][m], m6 < # wlar1, m < # vols1[v], m5 < # wlar1, m0 < # wlar1, bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(to-vtbl(vols1), buf), unique-sqns(apebs), 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, to-vtbl(vols1), q0), valid-global-sqn(apebs, m1), valid-global-sqn(apebs, n1), valid-peb(v0, m11, mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false)), valid-peb(v1, m17, mkpeb(aechdr(m16), avidhdr(v, m, valid-sqns(v1, m17, apebs).max, m13, m14), buf1, m15, false)), v ∈ vols1, v ∈ vols0, m6 < # apebs ∧ m5 < # apebs ∧ m6 ≠ m5 ∧ valid-peb(v, m, apebs[m6]) ∧ valid-peb(v, m, apebs[m5]) → (∃ bag. valid-sqns(v, m, apebs) = bag ++ apebs[m6].vidhdr.sqn ++ apebs[m5].vidhdr.sqn) ⊦ m5 = m6, m5 = m0, m6 = m0, VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 86:
# wlar0 = # wlar1, # apebs = # wlar1, # vols0[v] = # vols1[v], avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, wlar0[m6] = wl-entry(m16, used), apebs[m6] = mkpeb(aechdr(m16), avidhdr(v, m, valid-sqns(v1, m17, apebs).max, m13, m14), buf1, m15, false), wlar1[m5] = wl-entry(m10, used), apebs[m5] = mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false), wlar1[m0] = wl-entry(m4, used), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar0[m0] = wl-entry(m3, used), ⌜m6⌝ = vols0[v][m], ⌜m5⌝ = vols1[v][m], m6 < # wlar1, m < # vols1[v], m5 < # wlar1, m0 < # wlar1, bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(to-vtbl(vols1), buf), unique-sqns(apebs), 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, to-vtbl(vols1), q0), valid-global-sqn(apebs, m1), valid-global-sqn(apebs, n1), valid-peb(v0, m11, mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false)), valid-peb(v1, m17, mkpeb(aechdr(m16), avidhdr(v, m, valid-sqns(v1, m17, apebs).max, m13, m14), buf1, m15, false)), v ∈ vols1, v ∈ vols0, v1 = v ∧ m17 = m ∧ v0 = v ∧ m11 = m → valid-sqns(v, m, apebs) = bag ++ valid-sqns(v, m, apebs).max ++ valid-sqns(v, m, apebs).max ⊦ m5 = m6, m5 = m0, m6 = m0, VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0

Rule argument

Additional information

Used simplifier rules: ⊦ avidhdr(v, m, m0, m1, m2).sqn = m0; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)