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Proof step 163 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, n0 < # buf + # buf1, abs-node(buf1, a), abs-nodes(buf, m + # buf2, a0 ' + x0, @(m0, m1) ' + lax0, false), abs-nodes(subarray(buf + buf1, 0, n0), m + # buf2, (a0 ' + x0) + a ', (@(m0, m1) ' + lax0) + @(m + # buf2 + # buf, # buf1) ', boolvar), abs-padding(buf2), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n0 + # buf2, NODE_HEADER_SIZE), ∀ 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, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n0 < # buf + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes (subarray(buf + buf1, 0, n0), m + # buf2, (a0 ' + x0) + a ', (@(m0, m1) ' + lax0) + @((m + # buf2) + # buf, # buf1) ', boolvar) ∧ abs-nodes(buf, m + # buf2, a0 ' + x0, @(m0, m1) ' + lax0, false) ∧ is-aligned(n0, NODE_HEADER_SIZE) ∧ is-aligned(m + # buf2, NODE_HEADER_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 164:
# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, n0 < # buf + # buf1, abs-node(buf1, a), abs-nodes(subarray(buf + buf1, 0, n0), m + # buf2, (a0 ' + x0) + a ', (@(m0, m1) ' + lax0) + @(m + # buf2 + # buf, # buf1) ', boolvar), abs-nodes(buf, m + # buf2, a0 ' + x0, @(m0, m1) ' + lax0, false), abs-padding(buf2), is-aligned(n0 + # buf2, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), ∀ 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, is-aligned(n0, NODE_HEADER_SIZE) ∧ is-aligned(# buf2, NODE_HEADER_SIZE)

Rule argument

Additional information

Used simplifier rules: abs-nodes-unique-strong-h: ⊦ abs-nodes(buf, m, x0, lax0, false) → (abs-nodes(buf, m, x1, lax1, boolvar1) ↔ x0 = x1 ∧ lax0 = lax1);%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ abs-node(buf, nd0) → (abs-node(buf, nd1) ↔ nd0 = nd1); (s)