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Proof step 130 from proof refine-write (previous step)

LEB_SIZE = (n5 + n0) + n1 + n4, avols[default-volid][m2] = mapped(buf0, n4), n0 < n, 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), is-aligned(n1, EB_PAGE_SIZE), default-volid ∈ avols, n0 + n1 + n4 ≤ LEB_SIZE, n3 + n0 ≤ # buf, n1 + n4 ≤ LEB_SIZE, n4 ≤ LEB_SIZE, n3 + n ≤ # buf, (n1 + n4) + n ≤ LEB_SIZE, ⌊err1⌋ ⊦ subarray(buf0, 0, n4) + mkempbuf(n1) = subarray(buf0, 0, n1 + n4), n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 131:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 132:
LEB_SIZE = (n5 + n0) + n1 + n4, avols[default-volid][m2] = mapped(buf0, n4), m2 < # avols[default-volid], n0 < n, ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(n0, EB_PAGE_SIZE), default-volid ∈ avols, (n1 + n4) + n ≤ LEB_SIZE, n3 + n ≤ # buf, n4 ≤ LEB_SIZE, n1 + n4 ≤ LEB_SIZE, n3 + n0 ≤ # buf, n0 + n1 + n4 ≤ LEB_SIZE, ⌊err1⌋ ⊦ n0 = 0, #(subarray(buf0, 0, n4) + mkempbuf(n1)) = # subarray(buf0, 0, n1 + n4) ∧ (∀ n. n < #(subarray(buf0, 0, n4) + mkempbuf(n1)) → (subarray(buf0, 0, n4) + mkempbuf(n1))[n] = subarray(buf0, 0, n1 + n4)[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, n1 + n4), subarray(buf0, 0, n4) + mkempbuf(n1)] flags: <all paths>

Additional information

Used terms: subarray(buf0, 0, n1 + n4), subarray(buf0, 0, n4) + mkempbuf(n1)