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Proof step 30 from proof range-eq-validtrailer (previous step)

is-aligned(m, NODE_HEADER_SIZE), is-aligned(# buf, NODE_HEADER_SIZE), range=(buf, m, validtrailer, 0, NODE_HEADER_SIZE) ⊦ range=(buf + mkempbuf(n), m, validtrailer, 0, NODE_HEADER_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n])
Proof step 32:
is-aligned(# buf, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), range=(buf, m, validtrailer, 0, NODE_HEADER_SIZE) ⊦ m + NODE_HEADER_SIZE ≤ #(buf + mkempbuf(n)) ∧ 0 + NODE_HEADER_SIZE ≤ # validtrailer ∧ (∀ n2. n2 < NODE_HEADER_SIZE → (buf + mkempbuf(n))[m + n2] = (validtrailer)[0 + n2])

Rule argument

spec: array-splice, inst: buffer name: range-eq-ext seq: ⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n]) subst: [m, n1, buf0, n0, buf] → [NODE_HEADER_SIZE, 0, validtrailer, m, buf + mkempbuf(n)] flags: <all paths>

Additional information

Used terms: NODE_HEADER_SIZE, 0, validtrailer, m, buf + mkempbuf(n)