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Proof step 167 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf2 = a0.alignedsize + 2 * NODE_HEADER_SIZE, lax.head = @(m, # buf2), n0 < # buf + # buf1, abs-node(buf2, a0), abs-node(buf1, a), abs-nodes(buf, m + # buf2, x0, lax.tail, false), abs-nodes(buf2 + subarray(buf + buf1, 0, n0), m, (a0 ' + x0) + a ', lax + @(m + # buf2 + # buf, # buf1) ', boolvar), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n0, NODE_HEADER_SIZE), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf2 + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf3 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf3 + buf1, 0, n), m, x + a ', lax + @(m + # buf3, # buf1) ', boolvar) ∧ abs-nodes(buf3, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf3 + # buf1 ⊦ lax = [], n0 = # buf + # buf1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 168:
# buf2 = a0.alignedsize + 2 * NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, ladr = @(m, # buf2), lax = ladr + lax0, n0 < # buf + # buf1, abs-node(buf1, a), abs-node(buf2, a0), abs-nodes(buf2 + subarray(buf + buf1, 0, n0), m, (a0 ' + x0) + a ', lax + @(m + # buf2 + # buf, # buf1) ', boolvar), abs-nodes(buf, m + # buf2, x0, lax0, false), is-aligned(n0, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf2 + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf3 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf3 + buf1, 0, n), m, x + a ', lax + @(m + # buf3, # buf1) ', boolvar) ∧ abs-nodes(buf3, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf3 + # buf1 ⊦ lax = [], n0 = # buf + # buf1

Rule argument

spec: list-data, inst: laddress-list name: elim-list-c seq: lax ≠ [] ⊦ ladr = lax.head ∧ lax0 = lax.tail ↔ lax = ladr + lax0 subst: [lax, ladr, lax0] → [lax, ladr, lax0]

Additional information

Used simplifier rules: lax ≠ [] ⊦ ladr = lax.head ∧ lax0 = lax.tail ↔ lax = ladr + lax0; (elim) Used terms: lax, ladr, lax0