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Proof step 130 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) = n0 + m2, n2 ≠ 0, n3 ≠ 0, m2 < EB_PAGE_SIZE, m4 < # avol1, n2 < n0 + m2, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(n2, EB_PAGE_SIZE), is-aligned(n0 + m2, EB_PAGE_SIZE), is-aligned(# buf2, EB_PAGE_SIZE), # avol1[m4].data + n3 ≤ LEB_SIZE, n3 ≤ # buf3, EB_PAGE_SIZE ≤ m2 + n3, # buf2 + m2 + n3 ≤ LEB_SIZE, n0 ≤ # buf3, # buf2 + n0 + m2 ≤ LEB_SIZE, ⌊err1⌋ ⊦ m2 < n2 ∧ n2 ≠ m2 ∧ n2 < n3 + m2 ∧ is-aligned(# avol1[m4].data + (n2 - m2), EB_PAGE_SIZE) ∧ ⟨avol1[buffered(m4).leb] := mapped(avol1[buffered(m4).leb].data + subarray(buf3, 0, n2 - m2)); rofs := true⟩ ( abs (avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0[m4, mapped(avol0[m4].data + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n2))], true) ∧ rofs)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 131:
# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, n2 = n1 + m2, n2 < n0 + m2, 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(n0 + m2, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), # buf2 + n0 + m2 ≤ LEB_SIZE, n0 ≤ # buf3, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, m2 ≤ n2, ⌊err1⌋ ⊦ m2 < n2 ∧ n2 ≠ m2 ∧ n2 < n3 + m2 ∧ is-aligned(# avol1[m4].data + n1, EB_PAGE_SIZE) ∧ ⟨avol1[buffered(m4).leb] := mapped(avol1[buffered(m4).leb].data + subarray(buf3, 0, n1)); rofs := true⟩ ( abs (avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0[m4, mapped(avol0[m4].data + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n2))], true) ∧ rofs), n2 = 0, n3 = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n2, m2, n]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n < n0 → (n0 < n ↔ false); (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]% ⊦ m < n → n ≠ 0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%m ≠ 0 ⊦ is-aligned(n, m) → (n < m ↔ n = 0); (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n2, m2, n