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Proof step 33 from proof prepost-read-lebs (previous step)

# buf = (n2 + n1) * LEB_SIZE, avol[n3 + n1] = mapped(buf0), subarray(buf, 0, n1 * LEB_SIZE) = lebs(avol, n3, n1), n3 + n1 < # avol, ebm-vol-inv(avol), mapped-full?(avol, n3, n2 + n1), n1 * LEB_SIZE + LEB_SIZE ≤ # buf, n3 + n2 + n1 ≤ # avol, ⌊err0⌋ ⊦ n2 = 0, ∃ buf1. # buf1 = # buf ∧ range=(buf, 0, buf1, 0, n1 * LEB_SIZE) ∧ range=(buf, n1 * LEB_SIZE + LEB_SIZE, buf1, n1 * LEB_SIZE + LEB_SIZE, # buf - n1 * LEB_SIZE + LEB_SIZE)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 34:
# buf = (n2 + n1) * LEB_SIZE, # buf = n0 + n1 * LEB_SIZE + LEB_SIZE, avol[n3 + n1] = mapped(buf0), subarray(buf, 0, n1 * LEB_SIZE) = lebs(avol, n3, n1), n3 + n1 < # avol, ebm-vol-inv(avol), mapped-full?(avol, n3, n2 + n1), n3 + n2 + n1 ≤ # avol, n1 * LEB_SIZE + LEB_SIZE ≤ # buf, ⌊err0⌋ ⊦ n2 = 0, ∃ buf1. # buf1 = # buf ∧ range=(buf, 0, buf1, 0, n1 * LEB_SIZE) ∧ range=(buf, n1 * LEB_SIZE + LEB_SIZE, buf1, n1 * LEB_SIZE + LEB_SIZE, n0)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# buf, n1 * LEB_SIZE + LEB_SIZE, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # buf, n1 * LEB_SIZE + LEB_SIZE, n