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Proof step 9 from proof is-encoded-size (previous step)

# buf1 = ENCODED_NAT_SIZE, # buf0 = (# ns - 1) * ENCODED_NAT_SIZE, is-encoded(ns -- n, buf0), is-encoded(n, buf1), n ∈ ns, ∀ ns0, buf. # ns0 < # ns → is-encoded(ns0, buf) → # buf = # ns0 * ENCODED_NAT_SIZE ⊦ # ns = 0, ENCODED_NAT_SIZE + # buf0 = # ns * ENCODED_NAT_SIZE, ns = ∅

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [# ns, m]

Additional information

Used simplifier rules: ⊦ m + 1 ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m * (n + 1) = m * n + m; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m + n = m + n0 ↔ n = n0; (s)%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: # ns, m