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Proof step 5 from proof ebm-vol-inv-write (previous step)

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, mapped(buf)][n0].mapped? → # avol[n, mapped(buf)][n0].data ≤ LEB_SIZE ∧ is-aligned(# avol[n, mapped(buf)][n0].data, EB_PAGE_SIZE) ⊦ # buf ≤ LEB_SIZE ∧ is-aligned(# buf, EB_PAGE_SIZE)

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 6:
avol[n].mapped?, n < # avol, avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE), ∀ n0. n0 < # avol ∧ avol[n, mapped(buf)][n0].mapped? → # avol[n, mapped(buf)][n0].data ≤ LEB_SIZE ∧ is-aligned(# avol[n, mapped(buf)][n0].data, EB_PAGE_SIZE), ∀ n. n < # avol ∧ avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE) ⊦ # buf ≤ LEB_SIZE ∧ is-aligned(# buf, EB_PAGE_SIZE)
Proof step 8:
n < # avol, avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE), ∀ n0. n0 < # avol ∧ avol[n, mapped(buf)][n0].mapped? → # avol[n, mapped(buf)][n0].data ≤ LEB_SIZE ∧ is-aligned(# avol[n, mapped(buf)][n0].data, EB_PAGE_SIZE), ∀ n. n < # avol ∧ avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE) ⊦ avol[n].mapped?, # buf ≤ LEB_SIZE ∧ is-aligned(# buf, EB_PAGE_SIZE)

Rule argument

fma: avol[n].mapped?

Additional information

Used formulas: avol[n].mapped?