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Proof step 20 from proof prepost-encode-padding (previous step)

# buf = 2 * NODE_HEADER_SIZE + n0, # buf1 = # buf, subarray(buf1, NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0) = subarray(buf, NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0), is-aligned(n0, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(n0, true), subarray(buf1, 0, NODE_HEADER_SIZE)) ⊦ buf = mkbuf(0), copy(validtrailer, 0, buf1, NODE_HEADER_SIZE + n0, NODE_HEADER_SIZE) = subarray(buf1, 0, NODE_HEADER_SIZE) + subarray(buf1, NODE_HEADER_SIZE, n0) + validtrailer

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 22:
# buf1 = # buf, # buf = 2 * NODE_HEADER_SIZE + n0, subarray(buf1, NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0) = subarray(buf, NODE_HEADER_SIZE, NODE_HEADER_SIZE + n0), is-aligned(n0, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(n0, true), subarray(buf1, 0, NODE_HEADER_SIZE)) ⊦ buf = mkbuf(0), # copy(validtrailer, 0, buf1, NODE_HEADER_SIZE + n0, NODE_HEADER_SIZE) = #(subarray(buf1, 0, NODE_HEADER_SIZE) + subarray(buf1, NODE_HEADER_SIZE, n0) + validtrailer) ∧ (∀ n. n < # copy(validtrailer, 0, buf1, NODE_HEADER_SIZE + n0, NODE_HEADER_SIZE) → copy(validtrailer, 0, buf1, NODE_HEADER_SIZE + n0, NODE_HEADER_SIZE)[n] = (subarray(buf1, 0, NODE_HEADER_SIZE) + subarray(buf1, NODE_HEADER_SIZE, n0) + validtrailer)[n])

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [ subarray(buf1, 0, NODE_HEADER_SIZE) + subarray(buf1, NODE_HEADER_SIZE, n0) + validtrailer, copy (validtrailer, 0, buf1, NODE_HEADER_SIZE + n0, NODE_HEADER_SIZE)] flags: <all paths>

Additional information

Used terms: subarray(buf1, 0, NODE_HEADER_SIZE) + subarray(buf1, NODE_HEADER_SIZE, n0) + validtrailer, copy(validtrailer, 0, buf1, NODE_HEADER_SIZE + n0, NODE_HEADER_SIZE)