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Proof step 19 from proof ls-datasize-wear-level (previous step)

LEB_SIZE = n1 + m, subarray(buf, m, n1) = mkempbuf(n1), m < datasize(subarray(buf, 0, m) + subarray(buf, m, n1), LEB_SIZE), is-aligned(m, EB_PAGE_SIZE), m ≤ LEB_SIZE ⊦ ∃ buf0. subarray(buf, 0, m) + subarray(buf, m, n1) = mkempbuf(LEB_SIZE) + buf0, ∃ buf0. subarray(buf, m, n1) = mkempbuf(LEB_SIZE - m) + buf0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
LEB_SIZE = n1 + m, LEB_SIZE = n0 + m, subarray(buf, m, n1) = mkempbuf(n1), m < datasize(subarray(buf, 0, m) + subarray(buf, m, n1), LEB_SIZE), is-aligned(m, EB_PAGE_SIZE), m ≤ LEB_SIZE ⊦ ∃ buf0. subarray(buf, m, n1) = mkempbuf(n0) + buf0, ∃ buf0. subarray(buf, 0, m) + subarray(buf, m, n1) = mkempbuf(LEB_SIZE) + buf0

Rule argument

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

Additional information

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