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Proof step 23 from proof prepost-encode-lpt (previous step)

# buf0 = # buf, # lpt = n1 + n0, # buf = lptsize(n1 + n0, LEB_SIZE), subarray(buf0, 0, n0 * ENCODED_LPROPS_SIZE) = subarray(buf, 0, n0 * ENCODED_LPROPS_SIZE), subarray(buf0, n0 * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE, # buf - n0 * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE) = subarray(buf, n0 * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE, # buf - n0 * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE), n1 ≠ 0, is-encoded(lpt, buf, n0), n0 * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE ≤ # buf, err = ESUCCESS → is-encoded(lpt[n0], subarray(buf0, n0 * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)) ∧ m = ENCODED_LPROPS_SIZE, err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪n := n0 + 1⟫ ( n ≤ # lpt ∧ # buf = lptsize(# lpt, LEB_SIZE) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → is-encoded(lpt, buf0, n)) ∧ # lpt < n1 + n)

Heuristic symbolic execution applied rule assign right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ m + 1 ≤ n ↔ m < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ ¬ n < n; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%n < # lpt, # buf0 = # buf1, n * ENCODED_LPROPS_SIZE + ENCODED_LPROPS_SIZE ≤ # buf0 ⊦ subarray(buf0, 0, n * ENCODED_LPROPS_SIZE) = subarray(buf1, 0, n * ENCODED_LPROPS_SIZE) ∧ is-encoded(lpt, buf0, n) ∧ is-encoded (lpt[n], subarray(buf1, n * ENCODED_LPROPS_SIZE, ENCODED_LPROPS_SIZE)) → is-encoded(lpt, buf1, n + 1); (ss)