| n < # avol, ∀ n. n < # avol ∧ avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE) ⊦ (∀ n0. n0 < # avol ∧ avol[n, aleb][n0].mapped? → # avol[n, aleb][n0].data ≤ LEB_SIZE ∧ is-aligned(# avol[n, aleb][n0].data, EB_PAGE_SIZE)) ↔ (avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE)) → aleb.mapped? → # aleb.data ≤ LEB_SIZE ∧ is-aligned(# aleb.data, EB_PAGE_SIZE) |
aleb.mapped?, n < # avol, avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE), ∀ n. n < # avol ∧ avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE), ∀ n0. n0 < # avol ∧ avol[n, aleb][n0].mapped? → # avol[n, aleb][n0].data ≤ LEB_SIZE ∧ is-aligned(# avol[n, aleb][n0].data, EB_PAGE_SIZE) ⊦ # aleb.data ≤ LEB_SIZE ∧ is-aligned(# aleb.data, EB_PAGE_SIZE)
n < # avol, (avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE)) → aleb.mapped? → # aleb.data ≤ LEB_SIZE ∧ is-aligned(# aleb.data, EB_PAGE_SIZE), ∀ n. n < # avol ∧ avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE) ⊦ ∀ n0. n0 < # avol ∧ avol[n, aleb][n0].mapped? → # avol[n, aleb][n0].data ≤ LEB_SIZE ∧ is-aligned(# avol[n, aleb][n0].data, EB_PAGE_SIZE)