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Proof step 104 from proof prepost-write-once (previous step)

# apebs0 = # wlar, # apebs2 = # wlar0, n2 + m1 = n + n0, q0.head = eq-entry(m4, lref), LEB_SIZE = (n2 + m0) + m1, LEB_SIZE = (n0 + n) + m0, vols0[v][m] = unmapped, wlar0[vtblpnum1] = wl-entry(m5, free), apebs2[vtblpnum1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), n0 + m0 ≠ 0, n ≠ 0, vtblpnum2 ≠ vtblpnum1, aehdr.valid?, n < LEB_SIZE, n < m1, vtblpnum1 < # wlar0, m < # vols0[v], bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), id(apebs2, apebs0, mapped-pebs(vols0)), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), ubi-io-inv(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, n) + mkempbuf(n0), m0 + n, false)]), ubi-io-inv(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv(apebs0), ubi-io-inv(apebs2), unique-sqns(apebs0), unique-sqns(apebs2), valid-ebatbl(apebs0, wlar, vols0, vtblpnum2), valid-ebatbl(apebs2, wlar0, vols0, vtblpnum2), valid-eraseq(apebs0, q0), valid-eraseq(wlar, q0), valid-eraseq(q0), valid-eraseq(q1), valid-eraseq(wlar0, q1), valid-eraseq(apebs2, q1), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs2, sqnum), valid-vtbl(apebs0, vols0, wlar, vtblpnum2), valid-vtbl(apebs2, vols0, wlar0, vtblpnum2), valid-wl(apebs0, wlar), valid-wl(apebs2, wlar0), v ∈ vols0, n + m0 ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m2 + n ≤ # buf, m1 ≤ LEB_SIZE, m1 + m2 ≤ # buf, m0 + m1 ≤ LEB_SIZE, q1.lebrefs ⊆ q0.lebrefs, ⌊err0⌋ , ¬ vtblpnum2 ∈ q0, ¬ VTBL_VOLID ∈ vols0, ¬ vtblpnum2 ∈ q1, apebs0 = apebs2 ∧ wlar = wlar0 ∧ q0 = q1 ∨ id○(apebs0, apebs2, vtblpnum1) ∧ id○(wlar, wlar0, vtblpnum1) ∧ q0 = eq-entry(vtblpnum1, lref) ' + q1 ⊦ ⟪ubi_wl_put_peb#(v × m, vtblpnum1; wlar0, q1); skip⟫ ( # apebs2 = # wlar0 ∧ unique-sqns(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, n) + mkempbuf(n0), m0 + n, false)]) ∧ valid-global-sqn (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, n) + mkempbuf(n0), m0 + n, false)], sqnum + 1) ∧ valid-wl (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, n) + mkempbuf(n0), m0 + n, false)], wlar0) ∧ valid-eraseq(q1) ∧ valid-eraseq(wlar0, q1) ∧ valid-eraseq (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, n) + mkempbuf(n0), m0 + n, false)], q1) ∧ bflipset-cons(bflipset, wlar0) ∧ valid-ebatbl (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, n) + mkempbuf(n0), m0 + n, false)], wlar0, vols0, vtblpnum2) ∧ valid-vtbl(apebs2, vols0, wlar0, vtblpnum2) ∧ id (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, n) + mkempbuf(n0), m0 + n, false)], apebs0, mapped-pebs(vols0)) ∧ q1.lebrefs ⊆ q0.lebrefs ++ (v × m))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 105:
# apebs2 = # wlar0, # apebs0 = # wlar1, n2 + m1 = n + n0, q0.head = eq-entry(m4, lref0), LEB_SIZE = (n0 + n) + m0, LEB_SIZE = (n2 + m0) + m1, apebs2[vtblpnum1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar0[vtblpnum1] = wl-entry(m5, free), vols0[v][m] = unmapped, lref = v × m, q = q1, vtblpnum = vtblpnum1, wlar = wlar0, aehdr.valid?, m < # vols0[v], vtblpnum1 < # wlar0, n < m1, n < LEB_SIZE, bflipset-cons(bflipset, wlar0), bflipset-cons(bflipset, wlar1), id(apebs2, apebs0, mapped-pebs(vols0)), is-aligned(m0, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), ubi-io-inv(apebs2), ubi-io-inv(apebs0), ubi-io-inv(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, n) + mkempbuf(n0), m0 + n, false)]), unique-sqns(apebs2), unique-sqns(apebs0), valid-ebatbl(apebs2, wlar0, vols0, vtblpnum2), valid-ebatbl(apebs0, wlar1, vols0, vtblpnum2), valid-eraseq(apebs2, q1), valid-eraseq(wlar0, q1), valid-eraseq(q1), valid-eraseq(q0), valid-eraseq(wlar1, q0), valid-eraseq(apebs0, q0), valid-global-sqn(apebs2, sqnum), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs2, vols0, wlar0, vtblpnum2), valid-vtbl(apebs0, vols0, wlar1, vtblpnum2), valid-wl(apebs2, wlar0), valid-wl(apebs0, wlar1), v ∈ vols0, m0 + m1 ≤ LEB_SIZE, m1 + m2 ≤ # buf, m1 ≤ LEB_SIZE, m2 + n ≤ # buf, m0 ≤ LEB_SIZE, n + m0 ≤ LEB_SIZE, q1.lebrefs ⊆ q0.lebrefs, ⌊err0⌋ , apebs0 = apebs2 ∧ wlar1 = wlar0 ∧ q0 = q1 ∨ id○(apebs0, apebs2, vtblpnum1) ∧ id○(wlar1, wlar0, vtblpnum1) ∧ q0 = eq-entry(vtblpnum1, lref0) ' + q1 ⊦ ⟪wlar[vtblpnum].status := erasing; q := q + eq-entry(vtblpnum, lref); skip⟫ ( # apebs2 = # wlar ∧ unique-sqns(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, n) + mkempbuf(n0), m0 + n, false)]) ∧ valid-global-sqn (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, n) + mkempbuf(n0), m0 + n, false)], sqnum + 1) ∧ valid-wl(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, n) + mkempbuf(n0), m0 + n, false)], wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, n) + mkempbuf(n0), m0 + n, false)], q) ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, n) + mkempbuf(n0), m0 + n, false)], wlar, vols0, vtblpnum2) ∧ valid-vtbl(apebs2, vols0, wlar, vtblpnum2) ∧ id (apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, n) + mkempbuf(n0), m0 + n, false)], apebs0, mapped-pebs(vols0)) ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m)), n0 + m0 = 0, n = 0, vtblpnum2 = vtblpnum1, vtblpnum2 ∈ q0, VTBL_VOLID ∈ vols0, vtblpnum2 ∈ q1

Rule argument

pos: right 1

Additional information

Used simplifier rules: wl-put-peb: ⊦ ;