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Proof step 5 from proof abs-nodes-no-padding-rec (previous step)

# buf = (2 * NODE_HEADER_SIZE + a.alignedsize) + x.flashsize, lax.head = @(m0, m1) ⊦ abs-nodes(buf, m, a ' + x, lax, false) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ lax ≠ [] ∧ m0 = m ∧ m1 = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax.tail, false))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
# buf = (2 * NODE_HEADER_SIZE + a.alignedsize) + x.flashsize, ladr = @(m0, m1), lax = ladr + lax0 ⊦ abs-nodes(buf, m, a ' + x, lax, false) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ lax ≠ [] ∧ m0 = m ∧ m1 = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax0, false)), 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: abs-nodes-first-adr-explicit: ⊦ abs-nodes(buf, m, a ' + x, lax, weak) → (lax.head = ladr ↔ (∃ lax0. lax = ladr + lax0));%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ ladr + lax = ladr ' + lax; (s)% ⊦ 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: lax, ladr, lax0