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Proof step 46 from proof refine-write (previous step)

LEB_SIZE = (n4 + n) + n0 + n2, avols[default-volid][m2] = mapped(buf0, n2), m2 < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n, EB_PAGE_SIZE), is-aligned(n0, EB_PAGE_SIZE), default-volid ∈ avols, n + n0 + n2 ≤ LEB_SIZE, n0 + n2 ≤ LEB_SIZE, n2 ≤ LEB_SIZE, n3 + n ≤ # buf, (n0 + n2) + n ≤ LEB_SIZE ⊦ subarray(buf0, 0, n2) + mkempbuf(n0) = subarray(buf0, 0, n0 + n2), n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 48:
LEB_SIZE = (n4 + n) + n0 + n2, avols[default-volid][m2] = mapped(buf0, n2), m2 < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), default-volid ∈ avols, (n0 + n2) + n ≤ LEB_SIZE, n3 + n ≤ # buf, n2 ≤ LEB_SIZE, n0 + n2 ≤ LEB_SIZE, n + n0 + n2 ≤ LEB_SIZE ⊦ n = 0, #(subarray(buf0, 0, n2) + mkempbuf(n0)) = # subarray(buf0, 0, n0 + n2) ∧ (∀ n. n < #(subarray(buf0, 0, n2) + mkempbuf(n0)) → (subarray(buf0, 0, n2) + mkempbuf(n0))[n] = subarray(buf0, 0, n0 + n2)[n])

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [subarray(buf0, 0, n0 + n2), subarray(buf0, 0, n2) + mkempbuf(n0)] flags: <all paths>

Additional information

Used terms: subarray(buf0, 0, n0 + n2), subarray(buf0, 0, n2) + mkempbuf(n0)