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Proof step 51 from proof refine-write (previous step)

LEB_SIZE = (n4 + n) + n0 + n2, avols[default-volid][m2] = mapped(buf0, n2), n1 < LEB_SIZE, n1 < n2 + n0, m2 < # avols[default-volid], n1 < # subarray(buf0, 0, n2) + # mkempbuf(n0), 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 ⊦ (n1 < # subarray(buf0, 0, n2) ⊃ subarray(buf0, 0, n2)[n1];mkempbuf(n0)[n1 - # subarray(buf0, 0, n2)]) = buf0[n1], n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
LEB_SIZE = (n4 + n) + n0 + n2, avols[default-volid][m2] = mapped(buf0, n2), m2 < # avols[default-volid], n1 < LEB_SIZE, n1 < n2 + n0, 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 ⊦ (n1 < n2 ⊃ buf0[n1];mkempbuf(n0)[n1 - n2]) = buf0[n1], n = 0

Rule argument

Additional information

Used simplifier rules: ⊦ # mkempbuf(n) = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)% ⊦ # subarray(buf, m, n) = n; (s)