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Proof step 223 from proof refine-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n + m2, n3 ≠ 0, m4 < # avol1, m2 < EB_PAGE_SIZE, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), is-aligned(n + m2, EB_PAGE_SIZE), # buf2 + n + m2 ≤ LEB_SIZE, n ≤ # buf3, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, ⌊err1⌋ , ∀ n0. ¬ n0 < n + m2 ∨ ¬ is-aligned(n0, EB_PAGE_SIZE) ⊦ ∃ err0. (⌊err0⌋ ∨ err0 = ESUCCESS) ∧ ⟨err := err0; let m = buffered(m4).leb in {rofs := false; if err = ESUCCESS then avol1[m] := mapped(avol1[m].data + subarray(buf3, 0, n3)) else { choose n with n ≠ 0 ∧ n < n3 ∧ is-aligned(# avol1[m].data + n, EB_PAGE_SIZE) in avol1[m] := mapped(avol1[m].data + subarray(buf3, 0, n)) ifnone skip or skip; rofs := true}}⟩ (abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, true) ∧ rofs ∧ err1 = err)

User applied rule insert proof lemma

And obtained the following new goals

Proof step 224:
# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n + m2, n + m2 ≠ 0, n3 ≠ 0, m2 < EB_PAGE_SIZE, m4 < # avol1, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(n + m2, EB_PAGE_SIZE), is-aligned(# buf2, EB_PAGE_SIZE), n ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, n3 ≤ # buf3, EB_PAGE_SIZE ≤ m2 + n3, # buf2 + m2 + n3 ≤ LEB_SIZE, # buf2 + n + m2 ≤ LEB_SIZE, ⌊err1⌋ ⊦ ∃ err0. (⌊err0⌋ ∨ err0 = ESUCCESS) ∧ ⟨err := err0; let m = buffered(m4).leb in {rofs := false; if err = ESUCCESS then avol1[m] := mapped(avol1[m].data + subarray(buf3, 0, n3)) else { choose n with n ≠ 0 ∧ n < n3 ∧ is-aligned(# avol1[m].data + n, EB_PAGE_SIZE) in avol1[m] := mapped(avol1[m].data + subarray(buf3, 0, n)) ifnone skip or skip; rofs := true}}⟩ (abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, true) ∧ rofs ∧ err1 = err)

Rule argument

path: 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 subst: [avol0, avol1, lpt0, buf1, m4, buf2, m2, n3, n, buf3, err1] → [avol0, avol1, lpt0, buf1, m4, buf2, m2, n3, n, buf3, err1]

Additional information

Used simplifier rules: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ is-aligned(0, n); (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ n + 0 = n; (s)%n ≠ 0 ⊦ align↓(m, n) = 0 ↔ m < n; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)