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Proof step 7 from proof inv-map (previous step)

# apebs = # wlar, vols[v][vtblpnum1] = unmapped, vtblpnum1 < # vols[v], bflipset-cons(bflipset, wlar), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs, wlar), v ∈ vols, ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum ∈ q ⊦ ⟪ubi_write#(v, vtblpnum1, 0, 0, 0, mkbuf(0), EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum, sqnum, apebs; err)⟫ ( # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum) ∧ ubi-io-inv(apebs))

User applied rule insert program lemma

And obtained the following new goals

Proof step 8:
ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum), vtblpnum0 = EB_PAGE_SIZE, ubi-io-inv(apebs), v ∈ vols, vtblpnum1 < # vols[v], vtblpnum2 + n ≤ LEB_SIZE, n0 + n ≤ # buf, is-aligned(n, EB_PAGE_SIZE), is-aligned(vtblpnum2, EB_PAGE_SIZE), vols[v][vtblpnum1] ≠ unmapped → apebs[vols[v][vtblpnum1].pnum].fill ≤ vtblpnum2 ⊦ ⟪ubi_write#(v, vtblpnum1, vtblpnum2, n0, n, buf, vtblpnum0; vols, wlar, q, bflipset, vtblpnum, sqnum, apebs; err)⟫ (ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum) ∧ ubi-io-inv(apebs))

Rule argument

spec: <toplevel> name: inv-write seq: ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum), vtblpnum0 = EB_PAGE_SIZE, ubi-io-inv(apebs), v ∈ vols, vtblpnum1 < # vols[v], vtblpnum2 + n ≤ LEB_SIZE, n0 + n ≤ # buf, is-aligned(n, EB_PAGE_SIZE), is-aligned(vtblpnum2, EB_PAGE_SIZE), vols[v][vtblpnum1] ≠ unmapped → apebs[vols[v][vtblpnum1].pnum].fill ≤ vtblpnum2 ⊦ ⟪ubi_write# (v, vtblpnum1, vtblpnum2, n0, n, buf, vtblpnum0 ; vols, wlar, q, bflipset, vtblpnum, sqnum, apebs ; err)⟫ ( ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum) ∧ ubi-io-inv(apebs)) subst: [vtblpnum0, buf, n, n0, vtblpnum2, vtblpnum1, v, apebs, sqnum, vtblpnum, bflipset, q, wlar, vols, err] → [EB_PAGE_SIZE, mkbuf(0), 0, 0, 0, vtblpnum1, v, apebs, sqnum, vtblpnum, bflipset, q, wlar, vols, err] flags: <all paths>

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # mkbuf(n) = n; (s)% ⊦ 0 ≤ m; (s)%⊦ ubi-cons(apebs, vols, wlar, q, bflipset, n0, n1) ↔ # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, n1) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ valid-vtbl(apebs, vols, wlar, n0); (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ is-aligned(0, n); (s)