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Proof step 38 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][n1]) = abs(avols[default-volid][m, mapped(subarray(buf, 0, n) + mkempbuf(n0), n)])[n1], n1 = m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ n < # evol → abs(evol)[n] = abs(evol[n])

Rule argument

spec: ebm-vol-abs name: abs-at seq: ⊦ n < # evol → abs(evol)[n] = abs(evol[n]) subst: [n, evol] → [n1, avols[default-volid] [m, mapped(subarray(buf, 0, n) + mkempbuf(n0), n) ]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≠ n → evol[n, leb][m] = evol[m]; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ # evol[n, leb] = # evol; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s) Used terms: n1, avols[default-volid][m, mapped(subarray(buf, 0, n) + mkempbuf(n0), n)]