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Proof step 21 from proof prepost-decode-lpt (previous step)

# buf = lptsize(n1 + n0, LEB_SIZE), # lpt1 = n1 + n0, # lpt2 = n1 + n0, is-encoded(lp0, subarray(buf, n0 * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)), is-encoded(lpt1, buf, n0), n0 * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE ≤ # buf ⊦ n1 = 0, is-encoded(lpt1[n0, lp0], buf, n0 + 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ 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 23:
# lpt2 = n1 + n0, # lpt1 = n1 + n0, # buf = lptsize(n1 + n0, LEB_SIZE), is-encoded(lpt1, buf, n0), is-encoded(lp0, subarray(buf, n0 * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)), n0 * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE ≤ # buf ⊦ n1 = 0, # buf = lptsize(# lpt1[n0, lp0], LEB_SIZE) ∧ (∀ m. m < # lpt1[n0, lp0] ∧ m < n0 + 1 → is-encoded(lpt1[n0, lp0][m], subarray(buf, m * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)))

Rule argument

spec: encoding-lpt 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] → [n0 + 1, buf, lpt1[n0, lp0]] flags: <all paths>

Additional information

Used terms: n0 + 1, buf, lpt1[n0, lp0]