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Proof step 16 from proof abs-nodes-no-padding-last (previous step)

# buf1 = a0.alignedsize + 2 * NODE_HEADER_SIZE, # buf0 = (x0 + a ').flashsize, (lax + ladr ').head.size = # buf1, abs-node(buf1, a0), abs-nodes(buf0, (lax + ladr ').head.off + # buf1, x0 + a ', (lax + ladr ').tail, false), ∀ buf2, x, a, m, lax, ladr. # buf2 < #(buf1 + buf0) → # buf2 = (x + a ').flashsize ∧ abs-nodes(buf2, m, x + a ', lax + ladr ', false) → (∃ buf3, buf1. buf2 = buf3 + buf1 ∧ abs-nodes(buf3, m, x, lax, false) ∧ abs-node(buf1, a) ∧ ladr = @(# buf3 + m, 2 * NODE_HEADER_SIZE + a.alignedsize)) ⊦ ∃ buf3, buf2. buf1 + buf0 = buf3 + buf2 ∧ abs-nodes(buf3, (lax + ladr ').head.off, a0 ' + x0, lax, false) ∧ abs-node(buf2, a) ∧ ladr = @(# buf3 + (lax + ladr ').head.off, 2 * NODE_HEADER_SIZE + a.alignedsize)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
# buf0 = (x0 + a ').flashsize, # buf1 = a0.alignedsize + 2 * NODE_HEADER_SIZE, lax + ladr ' = ladr0 + lax0, ladr0.size = # buf1, abs-node(buf1, a0), abs-nodes(buf0, ladr0.off + # buf1, x0 + a ', lax0, false), ∀ buf2, x, a, m, lax, ladr. # buf2 < #(buf1 + buf0) → # buf2 = (x + a ').flashsize ∧ abs-nodes(buf2, m, x + a ', lax + ladr ', false) → (∃ buf3, buf1. buf2 = buf3 + buf1 ∧ abs-nodes(buf3, m, x, lax, false) ∧ abs-node(buf1, a) ∧ ladr = @(# buf3 + m, 2 * NODE_HEADER_SIZE + a.alignedsize)) ⊦ lax + ladr ' = [], ∃ buf3, buf2. buf1 + buf0 = buf3 + buf2 ∧ abs-nodes(buf3, ladr0.off, a0 ' + x0, lax, false) ∧ abs-node(buf2, a) ∧ ladr = @(# buf3 + ladr0.off, 2 * NODE_HEADER_SIZE + a.alignedsize)

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 ', ladr0, lax0]

Additional information

Used simplifier rules: ⊦ lax + lax0 = [] ↔ lax = [] ∧ lax0 = []; (as)% ⊦ ladr ' ≠ []; (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 ', ladr0, lax0