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Proof step 9 from proof refine-change (previous step)

# apebs0 = # wlar0, # apebs = # wlar, LEB_SIZE = n1 + n, vtblpnum < # vols[v], vtblpnum < # avols[v], abs(avols, apebs, vols, q), bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum1), valid-ebatbl(apebs, wlar, vols, vtblpnum0), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum0), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs0, vols0, wlar0, vtblpnum1), valid-vtbl(apebs, vols, wlar, vtblpnum0), valid-wl(apebs0, wlar0), valid-wl(apebs, wlar), v ∈ vols, v ∈ avols, n ≤ # buf, n ≤ LEB_SIZE, ¬ VTBL_VOLID ∈ vols, ¬ VTBL_VOLID ∈ vols0, err ≠ ESUCCESS → vols0 = vols ∧ id(apebs0, apebs, mapped-pebs(vols)) ∧ q0.lebrefs ⊆ q.lebrefs, err = ESUCCESS → q0.lebrefs ⊆ q.lebrefs ++ (v × vtblpnum) ∧ (vols[v][vtblpnum] ≠ unmapped → id(apebs0, apebs, mapped-pebs(vols) -- vols[v][vtblpnum].pnum)) ∧ (vols[v][vtblpnum] = unmapped → id(apebs0, apebs, mapped-pebs(vols))) ∧ vols0 = vols[v, vols[v][vtblpnum, ⌜n0⌝ ]] ∧ apebs0[n0].data = subarray(buf, 0, n) + mkempbuf(n1) ∧ apebs0[n0].fill = align↑(datasize(buf, n), EB_PAGE_SIZE), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟨ebm_change#(v, vtblpnum, n, buf; avols; err0)⟩ (abs(avols, apebs0, vols0, q0) ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
# apebs = # wlar, # apebs0 = # wlar0, LEB_SIZE = n1 + n, apebs0[n0] = mkpeb(aehdr, avhdr, buf0, m, boolvar), vtblpnum < # avols[v], vtblpnum < # vols[v], abs(avols, apebs, vols, q), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-inv(apebs0), unique-sqns(apebs), unique-sqns(apebs0), valid-ebatbl(apebs, wlar, vols, vtblpnum0), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-eraseq(apebs0, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs0, sqnum0), valid-vtbl(apebs, vols, wlar, vtblpnum0), valid-vtbl(apebs0, vols0, wlar0, vtblpnum1), valid-wl(apebs, wlar), valid-wl(apebs0, wlar0), v ∈ avols, v ∈ vols, n ≤ LEB_SIZE, n ≤ # buf, err = ESUCCESS → q0.lebrefs ⊆ q.lebrefs ++ (v × vtblpnum) ∧ (vols[v][vtblpnum] ≠ unmapped → id(apebs0, apebs, mapped-pebs(vols) -- vols[v][vtblpnum].pnum)) ∧ (vols[v][vtblpnum] = unmapped → id(apebs0, apebs, mapped-pebs(vols))) ∧ vols0 = vols[v, vols[v][vtblpnum, ⌜n0⌝ ]] ∧ buf0 = subarray(buf, 0, n) + mkempbuf(n1) ∧ m = align↑(datasize(buf, n), EB_PAGE_SIZE), err ≠ ESUCCESS → vols0 = vols ∧ id(apebs0, apebs, mapped-pebs(vols)) ∧ q0.lebrefs ⊆ q.lebrefs, err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟨ebm_change#(v, vtblpnum, n, buf; avols; err0)⟩ (abs(avols, apebs0, vols0, q0) ∧ err = err0), VTBL_VOLID ∈ vols, VTBL_VOLID ∈ vols0

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs0[n0], aehdr, avhdr, buf0, m, boolvar]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs0[n0], aehdr, avhdr, buf0, m, boolvar