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Proof step 9 from proof abs-nodes-one-h (previous step)

⊦ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ', lax, weak) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, lax.head.off + # buf0, [], lax.tail, weak))) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ', lax, weak) ∨ lax = @(m, 2 * NODE_HEADER_SIZE + a.alignedsize) ' ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, [], [], weak)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
lax = ladr + lax0 ⊦ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ', lax, weak) ∨ lax ≠ [] ∧ ladr.off = m ∧ ladr.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, ladr.off + # buf0, [], lax0, weak))) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ', lax, weak) ∨ lax = @(m, 2 * NODE_HEADER_SIZE + a.alignedsize) ' ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, [], [], weak))), lax = []

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: append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%⊦ buf0 + buf1 = buf2 + buf3 ∧ abs-padding(buf0) → (abs-padding(buf2) ↔ buf0 = buf2); (s)% ⊦ ladr ' ≠ []; (s)% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)%lax ≠ [] ⊦ ladr = lax.head ∧ lax0 = lax.tail ↔ lax = ladr + lax0; (elim) Used terms: lax, ladr, lax0