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Proof step 16 from proof encoding-shift (previous step)

# buf0 = # buf1, # buf1 = align↑(# lpt * ENCODED_LPROPS_SIZE, LEB_SIZE), subarray(buf0, 0, n * ENCODED_LPROPS_SIZE) = subarray(buf1, 0, n * ENCODED_LPROPS_SIZE), n0 < ENCODED_LPROPS_SIZE, m < # lpt, n < # lpt, is-encoded(lpt[n], subarray(buf1, n * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)), is-encoded(lpt[m], subarray(buf0, m * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)), m ≤ n, n * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE ≤ # buf1 ⊦ buf1[m * ENCODED_LPROPS_SIZE + n0] = buf0[m * ENCODED_LPROPS_SIZE + n0], is-encoded(lpt[m], subarray(buf1, m * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 18:
# subarray(buf0, 0, n * ENCODED_LPROPS_SIZE) = # subarray(buf1, 0, n * ENCODED_LPROPS_SIZE), # buf1 = align↑(# lpt * ENCODED_LPROPS_SIZE, LEB_SIZE), # buf0 = # buf1, n < # lpt, m < # lpt, n0 < ENCODED_LPROPS_SIZE, is-encoded(lpt[m], subarray(buf0, m * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)), is-encoded(lpt[n], subarray(buf1, n * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)), n * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE ≤ # buf1, m ≤ n, ∀ n0. n0 < # subarray(buf0, 0, n * ENCODED_LPROPS_SIZE) → subarray(buf0, 0, n * ENCODED_LPROPS_SIZE)[n0] = subarray(buf1, 0, n * ENCODED_LPROPS_SIZE)[n0] ⊦ buf1[m * ENCODED_LPROPS_SIZE + n0] = buf0[m * ENCODED_LPROPS_SIZE + n0], is-encoded(lpt[m], subarray(buf1, m * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE))

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, n * ENCODED_LPROPS_SIZE), subarray(buf0, 0, n * ENCODED_LPROPS_SIZE)] flags: <all paths>

Additional information

Used terms: subarray(buf1, 0, n * ENCODED_LPROPS_SIZE), subarray(buf0, 0, n * ENCODED_LPROPS_SIZE)