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Proof step 114 from proof abs-nodes-crash-h (previous step)

# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, lax.head = @(m, # buf1), abs-node(buf1, nd), abs-nodes(buf0, m + # buf1, x1, lax.tail, true), is-aligned(n, NODE_HEADER_SIZE), n ≤ # buf1 + # buf0, ∀ buf2, m, x, lax, n. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf2 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf2, 0, n), m, x0, lax0, true)) ⊦ lax = [], ∃ x, lax0. x ⊑ nd ' + x1 ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf1 + buf0, 0, n), m, x, lax0, true)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 115:
# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, ladr = @(m, # buf1), lax = ladr + lax1, abs-node(buf1, nd), abs-nodes(buf0, m + # buf1, x1, lax1, true), is-aligned(n, NODE_HEADER_SIZE), n ≤ # buf1 + # buf0, ∀ buf2, m, x, lax, n. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf2 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf2, 0, n), m, x0, lax0, true)) ⊦ lax = [], ∃ x, lax0. x ⊑ nd ' + x1 ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf1 + buf0, 0, n), m, x, lax0, true)

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, lax1]

Additional information

Used simplifier rules: lax ≠ [] ⊦ ladr = lax.head ∧ lax0 = lax.tail ↔ lax = ladr + lax0; (elim) Used terms: lax, ladr, lax1