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Proof step 55 from proof abs-nodes-add-crash-aligned-h (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 56:
⊦ (buf + buf0) + buf1 = buf + buf0 + buf1
Proof step 57:
# buf6 = NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf5 = NODE_HEADER_SIZE, subarray(buf5 + buf4 + validtrailer, 0, n) = buf6 + (buf + validtrailer) + buf0, n < 2 * NODE_HEADER_SIZE + # buf4, n < 2 * NODE_HEADER_SIZE + # buf4 + # buf2 + # buf1, abs-node(buf1, a), abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + # buf, a ', @(2 * NODE_HEADER_SIZE + m + # buf4 + # buf2, # buf1) ', boolvar), abs-nodes(buf2, 2 * NODE_HEADER_SIZE + m + # buf4, [], [], false), is-aligned(# buf4, 2 * NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf4, true), buf5), is-encoded(nodeheader(# buf, true), buf6), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #((buf5 + buf4 + validtrailer) + buf2) → # 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 ⊦ buf5 + buf4 + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + # buf4 + # buf2 + # buf1

Rule argument

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

Additional information

Used terms: buf0, buf + validtrailer, buf6