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Proof step 29 from proof abs-nodes-append-h (previous step)

lax0.head = @(m0, m1), (lax0 + lax1).head = @(m2, m3), m0 = m, m1 = # buf2, abs-node(buf2, nd), abs-nodes(buf, m + # buf2, x, lax0.tail, false), ∀ buf3, m, x0, lax0, buf1, x1, lax1, weak. # buf3 < #(buf2 + buf) → abs-nodes(buf3, m, x0, lax0, false) → (abs-nodes(buf3 + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf3, x1, lax1, weak)) ⊦ (∃ buf0, buf3. (buf2 + buf) + buf1 = buf0 + buf3 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf3, m + # buf0, nd ' + x + x1, lax0 + lax1, weak) ∨ lax0 + lax1 ≠ [] ∧ m2 = m ∧ m3 = # buf0 ∧ abs-node(buf0, nd) ∧ abs-nodes(buf3, m + # buf0, x + x1, (lax0 + lax1).tail, weak))) ↔ abs-nodes(buf1, m + # buf2 + # buf, x1, lax1, weak), lax0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
# buf2 = nd.alignedsize + 2 * NODE_HEADER_SIZE, lax0.head = @(m, # buf2), abs-node(buf2, nd), abs-nodes(buf, m + # buf2, x, lax0.tail, false), ∀ buf3, m, x0, lax0, buf1, x1, lax1, weak. # buf3 < #(buf2 + buf) → abs-nodes(buf3, m, x0, lax0, false) → (abs-nodes(buf3 + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf3, x1, lax1, weak)) ⊦ (∃ buf0, buf3. (buf2 + buf) + buf1 = buf0 + buf3 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf3, m + # buf0, nd ' + x + x1, lax0 + lax1, weak) ∨ lax0 + lax1 ≠ [] ∧ # buf2 = # buf0 ∧ abs-node(buf0, nd) ∧ abs-nodes(buf3, m + # buf0, x + x1, lax0.tail + lax1, weak))) ↔ abs-nodes(buf1, m + # buf2 + # buf, x1, lax1, weak), lax0 = []

Rule argument

Additional information

Used simplifier rules: ls-abs-node-buf-size: ⊦ abs-node(buf, nd) → # buf = nd.alignedsize + 2 * NODE_HEADER_SIZE;% ⊦ @(m, m0) = @(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ lax ≠ [] → (lax + lax0).tail = lax.tail + lax0; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ lax ≠ [] → (lax + lax0).head = lax.head; (s)