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Proof step 26 from proof prepost-decode-lpt (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ 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 28:
# buf = lptsize(# lpt1, LEB_SIZE), # buf = lptsize(n1 + n0, LEB_SIZE), # lpt1 = n1 + n0, # lpt2 = n1 + n0, m < n1 + n0, m < n0, is-encoded(lp0, subarray(buf, n0 * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)), n0 * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE ≤ # buf, ∀ m. m < # lpt1 ∧ m < n0 → is-encoded(lpt1[m], subarray(buf, m * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)) ⊦ m = n0, n1 = 0, is-encoded(lpt1[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, buf, lpt1] flags: <all paths>

Additional information

Used terms: n0, buf, lpt1