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Proof step 119 from proof refine-add-log-leb (previous step)

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

User applied rule all left

And closed the goal!

Rule argument

pos: left 13 terms: m abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ mapped(buf).mapped?; (s)% ⊦ 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 terms: m