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Proof step 30 from proof valid-wl-write-unmapped (previous step)

# apebs = # wlar, avhdr0.sqn = valid-sqns(v, m, apebs).max, avhdr1.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, apebs[n0] = mkpeb(aechdr(m6), avhdr1, buf1, m2, false), vols[avhdr.vol][avhdr.leb] = unmapped, wlar[n1] = wl-entry(m4, used), wlar[n] = wl-entry(m5, erasing), wlar[n0] = wl-entry(m6, used), apebs[n1] = mkpeb(aechdr(m4), avhdr0, buf0, m1, false), apebs[n] = mkpeb(aehdr0, avhdr2, buf2, m3, boolvar0), n1 < # wlar, n0 < # wlar, avhdr.leb < # vols[avhdr.vol], n < # wlar, is-encoded(to-vtbl(vols), buf1), valid-peb(v, m, mkpeb(aechdr(m4), avhdr0, buf0, m1, false)), valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m6), avhdr1, buf1, m2, false)), valid-peb(v, m, mkpeb(aehdr0, avhdr2, buf2, m3, boolvar0)), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), avhdr.vol ∈ vols, ∀ v, m, n2. vols[v][m] = ⌜n2⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n2].status = used ∧ n2 < # wlar ∧ apebs[n2].vidhdr.valid? ∧ apebs[n2].vidhdr.vol = v ∧ apebs[n2].vidhdr.leb = m ∧ n2 ≠ n0 ⊦ avhdr0.sqn = ((valid-sqns(v, m, apebs) -- avhdr2.sqn) ∪ {avhdr.sqn} ).max, n1 = n, VTBL_VOLID ∈ vols

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
# apebs = # wlar, avhdr0.sqn = valid-sqns(v, m, apebs).max, avhdr1.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, vols[v][m] = unmapped, wlar[n1] = wl-entry(m4, used), wlar[n] = wl-entry(m5, erasing), wlar[n0] = wl-entry(m6, used), apebs[n1] = mkpeb(aechdr(m4), avhdr0, buf0, m1, false), apebs[n] = mkpeb(aehdr0, avhdr2, buf2, m3, boolvar0), apebs[n0] = mkpeb(aechdr(m6), avhdr1, buf1, m2, false), m < # vols[v], n < # wlar, n1 < # wlar, n0 < # wlar, is-encoded(to-vtbl(vols), buf1), valid-peb(v, m, mkpeb(aechdr(m4), avhdr0, buf0, m1, false)), valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m6), avhdr1, buf1, m2, false)), valid-peb(v, m, mkpeb(aehdr0, avhdr2, buf2, m3, boolvar0)), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), v ∈ vols, ∀ v, m, n2. vols[v][m] = ⌜n2⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n2].status = used ∧ n2 < # wlar ∧ apebs[n2].vidhdr.valid? ∧ apebs[n2].vidhdr.vol = v ∧ apebs[n2].vidhdr.leb = m ∧ n2 ≠ n0 ⊦ avhdr0.sqn = ((valid-sqns(v, m, apebs) -- avhdr2.sqn) ++ avhdr.sqn).max, n1 = n, VTBL_VOLID ∈ vols

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%union-com: ⊦ bag ∪ bag2 = bag2 ∪ bag; from specification bag-union[nat-bag]%union-ass: ⊦ bag ∪ bag3 ∪ bag4 = (bag ∪ bag3) ∪ bag4; from specification bag-union[nat-bag]% ⊦ bag ∪ {n} = bag ++ n; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.leb = m; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.vol = v; (s)