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Proof step 41 from proof prepost-write-lebs (previous step)

# avol1 = n3 + n5 + n2 + n4, # buf = (n2 + n4) * LEB_SIZE, # avol0 = # avol1, lebs(avol0, n5, n4) = subarray(buf, 0, n4 * LEB_SIZE), n5 + n4 < # avol1, ebm-vol-inv(avol0), ebm-vol-inv(avol1), ebm-vol-inv(avol0[n5 + n4, mapped(mkbuf(0))]), ebm-vol-inv(avol0[n5 + n4, mapped(subarray(buf, n4 * LEB_SIZE, LEB_SIZE))]), is-aligned(LEB_SIZE, EB_PAGE_SIZE), mapped-full?(avol0, n5, n4), range=(avol0, 0, avol1, 0, n5), range=(avol0, n5 + n2 + n4, avol1, n5 + n2 + n4, n3), n5 + n2 + n4 ≤ # avol1, n4 * LEB_SIZE + LEB_SIZE ≤ # buf, 1 ≤ n2 ⊦ n3 + n2 = 0, lebs(avol0, n5, n4) + subarray(buf, n4 * LEB_SIZE, LEB_SIZE) = subarray(buf, 0, LEB_SIZE * n4 + LEB_SIZE), n2 = 0

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 4 flags: discard

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%⊦ n0 + n1 ≤ # buf → subarray(buf, 0, n0) + subarray(buf, n0, n1) = subarray(buf, 0, n0 + n1); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ subarray(buf, n0, n1) = subarray(buf, n0, n2) ↔ n1 = n2; (ss)%mult-c: ⊦ m * n = n * m; from specification nat-mult