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Proof step 148 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf0 = a0.alignedsize, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf3 = NODE_HEADER_SIZE, # buf5 = a0.alignedsize, # buf6 = NODE_HEADER_SIZE, subarray(buf3 + buf0 + validtrailer, 0, n) = (buf6 + buf5 + validtrailer) + buf2, n < 2 * NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1, n < 2 * NODE_HEADER_SIZE + a0.alignedsize, abs-node(buf1, a), abs-nodes(buf, 2 * NODE_HEADER_SIZE + m + a0.alignedsize, x0, lax0, false), abs-nodes (buf2, 2 * NODE_HEADER_SIZE + m + a0.alignedsize, x0 + a ', lax0 + @(2 * NODE_HEADER_SIZE + m + a0.alignedsize + # buf, # buf1) ', boolvar), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(a0), false), buf6), is-encoded(a0, subarray(buf5, 0, node-size-headerless(a0))), is-encoded(nodeheader(node-size-headerless(a0), false), buf3), is-encoded(a0, subarray(buf0, 0, node-size-headerless(a0))), ∀ buf4, buf1, a, n, m, x, lax, boolvar. # buf4 < #((buf3 + buf0 + validtrailer) + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf4 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf4 + buf1, 0, n), m, x + a ', lax + @(m + # buf4, # buf1) ', boolvar) ∧ abs-nodes(buf4, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf4 + # buf1 ⊦ buf6 + buf5 + validtrailer = mkbuf(0), buf3 + buf0 + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 149:
⊦ (buf + buf0) + buf1 = buf + buf0 + buf1
Proof step 150:
# buf6 = NODE_HEADER_SIZE, # buf5 = a0.alignedsize, # buf3 = NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf0 = a0.alignedsize, subarray(buf3 + buf0 + validtrailer, 0, n) = buf6 + (buf5 + validtrailer) + buf2, n < 2 * NODE_HEADER_SIZE + a0.alignedsize, n < 2 * NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1, abs-node(buf1, a), abs-nodes (buf2, 2 * NODE_HEADER_SIZE + m + a0.alignedsize, x0 + a ', lax0 + @(2 * NODE_HEADER_SIZE + m + a0.alignedsize + # buf, # buf1) ', boolvar), abs-nodes(buf, 2 * NODE_HEADER_SIZE + m + a0.alignedsize, x0, lax0, false), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), is-encoded(a0, subarray(buf0, 0, node-size-headerless(a0))), is-encoded(nodeheader(node-size-headerless(a0), false), buf3), is-encoded(a0, subarray(buf5, 0, node-size-headerless(a0))), is-encoded(nodeheader(node-size-headerless(a0), false), buf6), ∀ buf4, buf1, a, n, m, x, lax, boolvar. # buf4 < #((buf3 + buf0 + validtrailer) + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf4 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf4 + buf1, 0, n), m, x + a ', lax + @(m + # buf4, # buf1) ', boolvar) ∧ abs-nodes(buf4, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf4 + # buf1 ⊦ buf3 + buf0 + validtrailer = mkbuf(0), buf6 + buf5 + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + a0.alignedsize + # buf + # buf1

Rule argument

spec: array-splice, inst: buffer name: append-a seq: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1 subst: [buf1, buf0, buf] → [buf2, buf5 + validtrailer, buf6] flags: <all paths>

Additional information

Used terms: buf2, buf5 + validtrailer, buf6