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Proof step 6 from proof inv-synced-write-buf (previous step)

avol[n, mapped(buf)][n0] = mapped(buf1), avol[n] = mapped(buf0), n0 < # avol, n < # avol, is-aligned(# buf, EB_PAGE_SIZE), ∀ n0. n0 < # avol ∧ avol[n0].mapped? → # avol[n0].data ≤ LEB_SIZE ∧ (n0 ≠ n → is-aligned(# avol[n0].data, EB_PAGE_SIZE)) ⊦ is-aligned(# buf1, EB_PAGE_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ m ≠ n → avol[n, aleb][m] = avol[m]
Proof step 8:
avol[n] = mapped(buf0), avol[n0] = mapped(buf1), n < # avol, n0 < # avol, is-aligned(# buf, EB_PAGE_SIZE), ∀ n0. n0 < # avol ∧ avol[n0].mapped? → # avol[n0].data ≤ LEB_SIZE ∧ (n0 ≠ n → is-aligned(# avol[n0].data, EB_PAGE_SIZE)) ⊦ n0 = n, is-aligned(# buf1, EB_PAGE_SIZE)

Rule argument

spec: array, inst: avolume name: Put-other seq: ⊦ m ≠ n → avol[n, aleb][m] = avol[m] subst: [m, aleb, n, avol] → [n0, mapped(buf), n, avol] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s) Used terms: n0, mapped(buf), n, avol