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Proof step 8 from proof is-encoded-size (previous step)

# buf1 = ENCODED_NAT_SIZE, # buf0 = #(ns -- n) * ENCODED_NAT_SIZE, is-encoded(n, buf1), is-encoded(ns -- n, buf0), 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
# 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 = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ ns → #(ns -- n) = # ns - 1; (s)