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Proof step 6 from proof encoding-shift (previous step)

# buf0 = # buf1, subarray(buf0, 0, n * ENCODED_LPROPS_SIZE) = subarray(buf1, 0, n * ENCODED_LPROPS_SIZE), n < # lpt, is-encoded(lpt, buf0, n), is-encoded(lpt[n], subarray(buf1, n * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)), n * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE ≤ # buf1 ⊦ # buf1 = align↑(# lpt * ENCODED_LPROPS_SIZE, LEB_SIZE) ∧ (m < # lpt ∧ ¬ n < m → 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 7:
⊦ is-encoded(lpt, buf, n) ↔ # buf = lptsize(# lpt, LEB_SIZE) ∧ (∀ m. m < # lpt ∧ m < n → is-encoded(lpt[m], subarray(buf, m * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)))
Proof step 8:
# buf0 = lptsize(# lpt, LEB_SIZE), # buf0 = # buf1, subarray(buf0, 0, n * ENCODED_LPROPS_SIZE) = subarray(buf1, 0, n * ENCODED_LPROPS_SIZE), n < # lpt, is-encoded(lpt[n], subarray(buf1, n * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)), n * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE ≤ # buf1, ∀ m. m < # lpt ∧ m < n → is-encoded(lpt[m], subarray(buf0, m * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)) ⊦ # buf1 = align↑(# lpt * ENCODED_LPROPS_SIZE, LEB_SIZE) ∧ (m < # lpt ∧ ¬ n < m → is-encoded(lpt[m], subarray(buf1, m * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)))

Rule argument

spec: <toplevel> name: is-encoded seq: ⊦ is-encoded(lpt, buf, n) ↔ # buf = lptsize(# lpt, LEB_SIZE) ∧ (∀ m. m < # lpt ∧ m < n → is-encoded (lpt[m], subarray (buf, m * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE))) subst: [n, buf, lpt] → [n, buf0, lpt] flags: <all paths>

Additional information

Used terms: n, buf0, lpt