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Proof step 46 from proof refine-write-buf (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n + m2, ¬ rofs0, 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 + (m2 + n3) % EB_PAGE_SIZE ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, n3 ≤ # buf3, EB_PAGE_SIZE ≤ m2 + n3, # buf2 + m2 + n3 ≤ LEB_SIZE, n ≤ # buf3, # buf2 + n + m2 ≤ LEB_SIZE ⊦ ⟨awbuf_write_buf#(n3, buf3, adr0, m3, plog0, lpt0, ns0, buffered(m4); avol1, rofs0; err1)⟩ ( abs (avol1, buffered(m4), mkwbuf(copy(buf3, n, buf1, 0, (m2 + n3) % EB_PAGE_SIZE), # buf2 + n + m2, (m2 + n3) % EB_PAGE_SIZE), avol0[m4, mapped(avol0[m4].data + mkempbuf(# buf2 - # avol0[m4].data) + copy(buf3, 0, copy(buf1, 0, mkbuf(n + m2), 0, m2), m2, n))], false) ∧ ¬ rofs0 ∧ ESUCCESS = err1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 47:
# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, # buf2 = n0 + # avol0[m4].data, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n + m2, ¬ rofs0, 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, n + (m2 + n3) % EB_PAGE_SIZE ≤ # buf3, # avol0[m4].data ≤ # buf2 ⊦ ⟨awbuf_write_buf#(n3, buf3, adr0, m3, plog0, lpt0, ns0, buffered(m4); avol1, rofs0; err1)⟩ ( abs (avol1, buffered(m4), mkwbuf(copy(buf3, n, buf1, 0, (m2 + n3) % EB_PAGE_SIZE), # buf2 + n + m2, (m2 + n3) % EB_PAGE_SIZE), avol0[m4, mapped(avol0[m4].data + mkempbuf(n0) + copy(buf3, 0, copy(buf1, 0, mkbuf(n + m2), 0, m2), m2, n))], false) ∧ ¬ rofs0 ∧ ESUCCESS = err1), n + m2 = 0, n3 = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [# avol0[m4].data, # buf2, n0]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ ¬ n < n; (s)%n ≠ 0, m % n = 0 ⊦ align↓(m, n) = m; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # avol0[m4].data, # buf2, n0