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Proof step 171 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf2 = a0.alignedsize + 2 * NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, n0 < # buf + # buf1, abs-node(buf1, a), abs-node(buf2, a0), abs-nodes(buf, m + # buf2, x0, lax0, false), is-aligned(n0, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), ∃ buf0, buf3. buf2 + subarray(buf + buf1, 0, n0) = buf0 + buf3 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf3, m + # buf0, a0 ' + x0 + a ', (@(m, # buf2) ' + lax0) + @(m + # buf2 + # buf, # buf1) ', boolvar) ∨ (@(m, # buf2) ' + lax0) + @(m + # buf2 + # buf, # buf1) ' ≠ [] ∧ ((@(m, # buf2) ' + lax0) + @(m + # buf2 + # buf, # buf1) ').head.off = m ∧ ((@(m, # buf2) ' + lax0) + @(m + # buf2 + # buf, # buf1) ').head.size = # buf0 ∧ abs-node(buf0, a0) ∧ abs-nodes(buf3, m + # buf0, x0 + a ', ((@(m, # buf2) ' + lax0) + @(m + # buf2 + # buf, # buf1) ').tail, boolvar)), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf2 + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf3 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf3 + buf1, 0, n), m, x + a ', lax + @(m + # buf3, # buf1) ', boolvar) ∧ abs-nodes(buf3, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf3 + # buf1 ⊦ n0 = # buf + # buf1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 172:
# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf3 = a0.alignedsize + 2 * NODE_HEADER_SIZE, n0 < # buf + # buf1, abs-node(buf3, a0), abs-node(buf1, a), abs-nodes(buf, m + # buf3, x0, lax0, false), abs-nodes(subarray(buf + buf1, 0, n0), m + # buf3, x0 + a ', lax0 + @(m + # buf3 + # buf, # buf1) ', boolvar), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n0, NODE_HEADER_SIZE), ∀ buf0, buf1, a, n, m, x, lax, boolvar. # buf0 < #(buf3 + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf0 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf0 + buf1, 0, n), m, x + a ', lax + @(m + # buf0, # buf1) ', boolvar) ∧ abs-nodes(buf0, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf0 + # buf1 ⊦ n0 = # buf + # buf1

Rule argument

Additional information

Used simplifier rules: ls-abs-node-buf-size: ⊦ abs-node(buf, nd) → # buf = nd.alignedsize + 2 * NODE_HEADER_SIZE;% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)% ⊦ (ladr ' + lax).tail = lax; (s)%⊦ abs-node(buf0, nd0) ∧ buf0 + buf2 = buf1 + buf3 → (abs-node(buf1, nd1) ↔ buf0 = buf1 ∧ nd0 = nd1); (s)% ⊦ @(m, m0).size = m0; (s)% ⊦ @(m, m0).off = m; (s)% ⊦ (ladr ' + lax).head = ladr; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ ladr ' + lax ≠ []; (s)% ⊦ abs-node(buf0, nd) ∧ buf0 + buf1 = buf + buf2 → ¬ abs-padding(buf); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]