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Proof step 51 from proof vols-is-max-is-max-vols (previous step)

# vols0[v] = # vols1[v], # apebs = # wlar1, # wlar0 = # wlar1, avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, wlar0[m5] = wl-entry(m12, stat), wlar0[m0] = wl-entry(m3, used), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar1[m0] = wl-entry(m4, used), apebs[m5] = mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false), wlar1[m5] = wl-entry(m10, used), unmapped = vols0[v][m], ⌜m5⌝ = vols1[v][m], m0 < # wlar1, m < # vols1[v], m5 < # wlar1, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset1, wlar1), is-encoded(to-vtbl(vols1), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, 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, to-vtbl(vols1), q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), valid-peb(v0, m11, mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false)), v ∈ vols0, v ∈ vols1, stat ≠ erasing → m10 = m12, stat = used → v0 = v1 ∧ m11 = m6 ⊦ m5 = m0, stat = free, stat = erroneous, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1

User applied rule constructor cut

And obtained the following new goals

Proof step 52:
# wlar0 = # wlar1, # apebs = # wlar1, # vols0[v] = # vols1[v], avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, 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), wlar0[m5] = wl-entry(m12, stat), stat = used, unmapped = vols0[v][m], ⌜m5⌝ = vols1[v][m], m5 < # wlar1, m < # vols1[v], m0 < # wlar1, bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(to-vtbl(vols1), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, m0), 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)), v ∈ vols1, v ∈ vols0, stat = used → v0 = v1 ∧ m11 = m6, stat ≠ erasing → m10 = m12 ⊦ m5 = m0, stat = erroneous, stat = free, VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0
Proof step 57:
# wlar0 = # wlar1, # apebs = # wlar1, # vols0[v] = # vols1[v], avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, 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), wlar0[m5] = wl-entry(m12, stat), stat = erasing, unmapped = vols0[v][m], ⌜m5⌝ = vols1[v][m], m5 < # wlar1, m < # vols1[v], m0 < # wlar1, bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(to-vtbl(vols1), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, m0), 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)), v ∈ vols1, v ∈ vols0, stat = used → v0 = v1 ∧ m11 = m6, stat ≠ erasing → m10 = m12 ⊦ m5 = m0, stat = erroneous, stat = free, VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0

Rule argument

var: stat

Additional information

Used simplifier rules: wlstatus freely generated by used, free, erroneous, erasing;;