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Proof step 377 from proof prepost-atomic-leb-change (previous step)

# apebs0 = # wlar, LEB_SIZE = n2 + n0, apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[n1] = wl-entry(m1, free), vols[v][m0] = ⌜m⌝ , wlar[m] = wl-entry(m2, stat), q0 = q, stat = used, aehdr.valid?, m < # wlar, n1 < # wlar, m0 < # vols[v], bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-peb(v, m0, apebs0[m]), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), v ∈ vols, n0 ≤ LEB_SIZE ⊦ ⟪ubi_wl_put_peb#(v × m0, m; wlar, q); bflipset := bflipset -- m; vols1 := vols[v, vols[v][m0, ⌜n1⌝ ]]; wlar[n1] := wl-entry(wlar[n1].ec, used)⟫ ( # apebs0 = # wlar ∧ unique-sqns(apebs0[n1, apebs0[n1].vidhdr:= avidhdr(v, m0, sqnum, 0, 0)]) ∧ valid-global-sqn(apebs0[n1, apebs0[n1].vidhdr:= avidhdr(v, m0, sqnum, 0, 0)], sqnum + 1) ∧ valid-wl(apebs0[n1, apebs0[n1].vidhdr:= avidhdr(v, m0, sqnum, 0, 0)], wlar) ∧ valid-eraseq(q0 + eq-entry(m, v × m0) ') ∧ valid-eraseq(wlar, q0 + eq-entry(m, v × m0) ') ∧ valid-eraseq(apebs0[n1, apebs0[n1].vidhdr:= avidhdr(v, m0, sqnum, 0, 0)], q0 + eq-entry(m, v × m0) ') ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs0[n1, apebs0[n1].vidhdr:= avidhdr(v, m0, sqnum, 0, 0)], wlar, vols[v, vols[v][m0, ⌜n1⌝ ]], vtblpnum1) ∧ valid-vtbl(apebs0, vols, wlar, vtblpnum1) ∧ q = q0 + eq-entry(m, v × m0) ' ∧ id(apebs0[n1, apebs0[n1].vidhdr:= avidhdr(v, m0, sqnum, 0, 0)], apebs0, mapped-pebs(vols)) ∧ vols1 = vols[v, vols[v][m0, ⌜n1⌝ ]] ∧ apebs0[n1].data = mkempbuf(LEB_SIZE)), m = vtblpnum1, vtblpnum1 = n1, vtblpnum1 ∈ q, VTBL_VOLID ∈ vols

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 378:
# apebs0 = # wlar, LEB_SIZE = n2 + n0, wlar[m] = wl-entry(m2, used), vols[v][m0] = ⌜m⌝ , wlar[n1] = wl-entry(m1, free), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), q0 = q, m ≠ vtblpnum1, vtblpnum1 ≠ n1, aehdr.valid?, m0 < # vols[v], n1 < # wlar, m < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-global-sqn(apebs0, sqnum), valid-peb(v, m0, apebs0[m]), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), v ∈ vols, n0 ≤ LEB_SIZE, ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum1 ∈ q, ¬ m ∈ q ⊦ ⟪ubi_wl_put_peb#(v × m0, m; wlar, q); bflipset := bflipset -- m; vols1 := vols[v, vols[v][m0, ⌜n1⌝ ]]; wlar[n1] := wl-entry(wlar[n1].ec, used)⟫ ( # apebs0 = # wlar ∧ unique-sqns(apebs0[n1, apebs0[n1].vidhdr:= avidhdr(v, m0, sqnum, 0, 0)]) ∧ valid-global-sqn(apebs0[n1, apebs0[n1].vidhdr:= avidhdr(v, m0, sqnum, 0, 0)], sqnum + 1) ∧ valid-wl(apebs0[n1, apebs0[n1].vidhdr:= avidhdr(v, m0, sqnum, 0, 0)], wlar) ∧ valid-eraseq(q0 + eq-entry(m, v × m0) ') ∧ valid-eraseq(wlar, q0 + eq-entry(m, v × m0) ') ∧ valid-eraseq(apebs0[n1, apebs0[n1].vidhdr:= avidhdr(v, m0, sqnum, 0, 0)], q0 + eq-entry(m, v × m0) ') ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs0[n1, apebs0[n1].vidhdr:= avidhdr(v, m0, sqnum, 0, 0)], wlar, vols[v, vols[v][m0, ⌜n1⌝ ]], vtblpnum1) ∧ valid-vtbl(apebs0, vols, wlar, vtblpnum1) ∧ q = q0 + eq-entry(m, v × m0) ' ∧ id(apebs0[n1, apebs0[n1].vidhdr:= avidhdr(v, m0, sqnum, 0, 0)], apebs0, mapped-pebs(vols)) ∧ vols1 = vols[v, vols[v][m0, ⌜n1⌝ ]] ∧ apebs0[n1].data = mkempbuf(LEB_SIZE))

Rule argument

Additional information

Used simplifier rules: lf-used-info: ⊦ n < # wlar ∧ wlar[n] = wl-entry(m, used) ∧ valid-eraseq(wlar, q) → ¬ n ∈ q;