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Proof step 30 from proof abs-nodes-unique-strong-h (previous step)

# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf1, nd), abs-nodes(buf0, m + # buf1, x, lax2, false), ∀ buf2, m, x0, lax0, x1, lax1, boolvar1. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x0, lax0, false) → (abs-nodes(buf2, m, x1, lax1, boolvar1) ↔ x0 = x1 ∧ lax0 = lax1) ⊦ lax1 ≠ [] ∧ lax1.head.off = m ∧ lax1.head.size = # buf1 ∧ nd = nd0 ∧ abs-nodes(buf0, lax1.head.off + # buf1, x2, lax1.tail, boolvar1) ↔ nd ' + x = nd0 ' + x2 ∧ @(m, # buf1) ' + lax2 = lax1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 31:
# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, lax1 = ladr + lax3, abs-node(buf1, nd), abs-nodes(buf0, m + # buf1, x, lax2, false), ∀ buf2, m, x0, lax0, x1, lax1, boolvar1. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x0, lax0, false) → (abs-nodes(buf2, m, x1, lax1, boolvar1) ↔ x0 = x1 ∧ lax0 = lax1) ⊦ lax1 ≠ [] ∧ ladr.off = m ∧ ladr.size = # buf1 ∧ nd = nd0 ∧ abs-nodes(buf0, ladr.off + # buf1, x2, lax3, boolvar1) ↔ nd ' + x = nd0 ' + x2 ∧ @(m, # buf1) ' + lax2 = lax1, lax1 = []

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] → [lax1, ladr, lax]

Additional information

Used simplifier rules: ⊦ ladr ' + lax ≠ []; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%lax ≠ [] ⊦ ladr = lax.head ∧ lax0 = lax.tail ↔ lax = ladr + lax0; (elim) Used terms: lax1, ladr, lax