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Proof step 80 from proof refine-move-buf (previous step)

# buf = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m5] = mapped(buf0), avol0[m] = mapped(buf1), m < # avol1, m5 < # avol1, m3 < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), is-aligned(# avol1[m].data, EB_PAGE_SIZE), is-aligned(# buf1, EB_PAGE_SIZE), ∀ n. n < # avol1 → (n ≠ m → avol1[n] = avol0[n]) ∧ (n = m → avol1[m] = mapped(buf1 + subarray(buf, 0, m3))) ⊦ m = m5, m3 = 0

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 81:
# avol0 = # avol1, # lpt0 = # avol1, # buf = EB_PAGE_SIZE, avol0[m] = mapped(buf1), avol0[m5] = mapped(buf0), m3 < EB_PAGE_SIZE, m5 < # avol1, m < # avol1, awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), is-aligned(# buf1, EB_PAGE_SIZE), is-aligned(# avol1[m].data, EB_PAGE_SIZE), ∀ n. n < # avol1 → (n ≠ m → avol1[n] = avol0[n]) ∧ (n = m → avol1[m] = mapped(buf1 + subarray(buf, 0, m3))) ⊦ avol1[m] = mapped(buf1 + subarray(buf, 0, m3)), m = m5, m3 = 0

Rule argument

fma: avol1[m] = mapped(buf1 + subarray(buf, 0, m3))

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # subarray(buf, m, n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ EB_PAGE_SIZE ≠ 0; (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%m ≠ 0 ⊦ is-aligned(n, m) → (n < m ↔ n = 0); (s) Used formulas: avol1[m] = mapped(buf1 + subarray(buf, 0, m3))