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Proof step 19 from proof abs-nodes-split-h (previous step)

# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, lax.head = @(m, # buf1), abs-node(buf1, nd), abs-nodes(buf0, m + # buf1, x + x1, lax.tail, weak), ∀ buf2, m, x0, x1, lax, weak. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x0 + x1, lax, weak) → (∃ buf3, buf1, lax0, lax1. lax = lax0 + lax1 ∧ buf2 = buf3 + buf1 ∧ abs-nodes(buf3, m, x0, lax0, false) ∧ abs-nodes(buf1, m + # buf3, x1, lax1, weak)) ⊦ lax = [], ∃ buf3, buf2, lax0, lax1. lax = lax0 + lax1 ∧ buf1 + buf0 = buf3 + buf2 ∧ abs-nodes(buf3, m, nd ' + x, lax0, false) ∧ abs-nodes(buf2, m + # buf3, x1, lax1, weak)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, ladr = @(m, # buf1), lax = ladr + lax2, abs-node(buf1, nd), abs-nodes(buf0, m + # buf1, x + x1, lax2, weak), ∀ buf2, m, x0, x1, lax, weak. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x0 + x1, lax, weak) → (∃ buf3, buf1, lax0, lax1. lax = lax0 + lax1 ∧ buf2 = buf3 + buf1 ∧ abs-nodes(buf3, m, x0, lax0, false) ∧ abs-nodes(buf1, m + # buf3, x1, lax1, weak)) ⊦ lax = [], ∃ buf3, buf2, lax0, lax1. lax = lax0 + lax1 ∧ buf1 + buf0 = buf3 + buf2 ∧ abs-nodes(buf3, m, nd ' + x, lax0, false) ∧ abs-nodes(buf2, m + # buf3, x1, lax1, weak)

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, lax2]

Additional information

Used simplifier rules: lax ≠ [] ⊦ ladr = lax.head ∧ lax0 = lax.tail ↔ lax = ladr + lax0; (elim) Used terms: lax, ladr, lax2