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Proof step 8 from proof awbuf-inv-crash (previous step)

# avol1 = # avol0, avol1[n] = mapped(buf), n < # avol0, bleb ≠ nobuffer → bleb.leb < # avol0 ∧ avol0[bleb.leb].mapped?, ∀ n. n < # avol0 → (avol0[n].mapped? → avol1[n] = mapped(subarray(avol0[n].data, 0, align↓(# avol0[n].data, EB_PAGE_SIZE)))) ∧ (¬ avol0[n].mapped? ∧ avol1[n].mapped? → # avol1[n].data ≤ LEB_SIZE ∧ is-aligned(# avol1[n].data, EB_PAGE_SIZE)), ∀ n. n < # avol0 ∧ avol0[n].mapped? → # avol0[n].data ≤ LEB_SIZE ∧ (buffered(n) ≠ bleb → is-aligned(# avol0[n].data, EB_PAGE_SIZE)) ⊦ is-aligned(# buf, EB_PAGE_SIZE)

User applied rule all left

And closed the goal!

Rule argument

pos: left 5 terms: n abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%m ≠ 0 ⊦ is-aligned(align↓(n, m), m); (s) Used terms: n