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Proof step 62 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf6 = NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf5 = NODE_HEADER_SIZE, buf5 + subarray(buf4 + validtrailer, 0, n0) = buf6 + (buf + validtrailer) + buf0, n0 < NODE_HEADER_SIZE + # buf4, 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(n0, 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 ⊦ NODE_HEADER_SIZE + # buf4 + # buf2 + # buf1 = n0, buf5 + buf4 + validtrailer = mkbuf(0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 63:
⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2)
Proof step 64:
# buf5 = NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf6 = NODE_HEADER_SIZE, # buf5 = # buf6, buf5 = buf6, subarray(buf4 + validtrailer, 0, n0) = (buf + validtrailer) + buf0, n0 < 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(n0, 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), NODE_HEADER_SIZE + # buf4 + # buf2 + # buf1 = n0

Rule argument

spec: array-splice, inst: buffer name: append-inj seq: ⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2) subst: [buf2, buf0, buf1, buf] → [(buf + validtrailer) + buf0, buf6, subarray(buf4 + validtrailer, 0, n0), buf5] flags: <all paths>

Additional information

Used terms: (buf + validtrailer) + buf0, buf6, subarray(buf4 + validtrailer, 0, n0), buf5