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Proof step 32 from proof refine-change (previous step)

LEB_SIZE = n0 + n, m < # avols[default-volid], n1 < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n, EB_PAGE_SIZE), default-volid ∈ avols, n ≤ LEB_SIZE, n ≤ # buf ⊦ abs(avols[default-volid])[m, mapped(subarray(buf, 0, n))][n1] = abs(avols[default-volid][m, mapped(subarray(buf, 0, n) + mkempbuf(n0), n)])[n1]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ m ≠ n → avol[n, aleb][m] = avol[m]
Proof step 34:
LEB_SIZE = n0 + n, n1 = m, n1 < # avols[default-volid], m < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n, EB_PAGE_SIZE), default-volid ∈ avols, n ≤ # buf, n ≤ LEB_SIZE ⊦ abs(avols[default-volid])[m, mapped(subarray(buf, 0, n))][n1] = abs(avols[default-volid][m, mapped(subarray(buf, 0, n) + mkempbuf(n0), n)])[n1]
Proof step 37:
LEB_SIZE = n0 + n, n1 < # avols[default-volid], m < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n, EB_PAGE_SIZE), default-volid ∈ avols, n ≤ # buf, n ≤ LEB_SIZE ⊦ abs(avols[default-volid])[n1] = abs(avols[default-volid][m, mapped(subarray(buf, 0, n) + mkempbuf(n0), n)])[n1], n1 = m

Rule argument

spec: array, inst: avolume name: Put-other seq: ⊦ m ≠ n → avol[n, aleb][m] = avol[m] subst: [m, aleb, n, avol] → [n1, mapped(subarray(buf, 0, n)), m, abs(avols[default-volid])] flags: <all paths>

Additional information

Used terms: n1, mapped(subarray(buf, 0, n)), m, abs(avols[default-volid])