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Proof step 28 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf0 = NODE_HEADER_SIZE, # buf = a.alignedsize, # buf4 = NODE_HEADER_SIZE, buf0 + subarray(buf + validtrailer, 0, n0) = (buf4 + buf3 + validtrailer) + buf1, n0 < NODE_HEADER_SIZE + a.alignedsize, abs-nodes(buf1, 2 * NODE_HEADER_SIZE + m + # buf3, a ', @(m, 2 * NODE_HEADER_SIZE + a.alignedsize) ', boolvar), is-aligned(# buf3, 2 * NODE_HEADER_SIZE), is-aligned(n0, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-encoded(nodeheader(# buf3, true), buf4), is-encoded(a, subarray(buf, 0, node-size-headerless(a))), is-encoded(nodeheader(node-size-headerless(a), false), buf0), ∀ buf, buf1, a, n, m, x, lax, boolvar. # buf < # mkbuf(0) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf + buf1, 0, n), m, x + a ', lax + @(m + # buf, # buf1) ', boolvar) ∧ abs-nodes(buf, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf + # buf1 ⊦ NODE_HEADER_SIZE + a.alignedsize = n0, buf0 + buf + validtrailer = mkbuf(0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ (buf + buf0) + buf1 = buf + buf0 + buf1
Proof step 30:
# buf4 = NODE_HEADER_SIZE, # buf = a.alignedsize, # buf0 = NODE_HEADER_SIZE, buf0 + subarray(buf + validtrailer, 0, n0) = buf4 + (buf3 + validtrailer) + buf1, n0 < NODE_HEADER_SIZE + a.alignedsize, abs-nodes(buf1, 2 * NODE_HEADER_SIZE + m + # buf3, a ', @(m, 2 * NODE_HEADER_SIZE + a.alignedsize) ', boolvar), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n0, NODE_HEADER_SIZE), is-aligned(# buf3, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(a), false), buf0), is-encoded(a, subarray(buf, 0, node-size-headerless(a))), is-encoded(nodeheader(# buf3, true), buf4), ∀ buf, buf1, a, n, m, x, lax, boolvar. # buf < # mkbuf(0) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf + buf1, 0, n), m, x + a ', lax + @(m + # buf, # buf1) ', boolvar) ∧ abs-nodes(buf, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf + # buf1 ⊦ buf0 + buf + validtrailer = mkbuf(0), NODE_HEADER_SIZE + a.alignedsize = n0

Rule argument

spec: array-splice, inst: buffer name: append-a seq: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1 subst: [buf1, buf0, buf] → [buf1, buf3 + validtrailer, buf4] flags: <all paths>

Additional information

Used terms: buf1, buf3 + validtrailer, buf4