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Proof step 3 from proof is-encoded-split-one (previous step)

# buf0 = # ns * ENCODED_NAT_SIZE, # buf1 = ENCODED_NAT_SIZE, is-encoded(n, buf1), is-encoded(ns, buf0) ⊦ is-encoded(ns1, buf0 + buf1) ↔ ns1 = ns ++ n, n ∈ ns

User applied rule induction

And obtained the following new goals

Proof step 4:
# buf0 = # ns * ENCODED_NAT_SIZE, # buf1 = ENCODED_NAT_SIZE, is-encoded(n, buf1), is-encoded(ns, buf0), ∀ ns0, buf0, ns, buf1, n. # ns0 < # ns1 → # buf0 = # ns * ENCODED_NAT_SIZE ∧ # buf1 = ENCODED_NAT_SIZE ∧ is-encoded(n, buf1) ∧ is-encoded(ns, buf0) → (is-encoded(ns0, buf0 + buf1) ↔ ns0 = ns ++ n) ∨ n ∈ ns ⊦ is-encoded(ns1, buf0 + buf1) ↔ ns1 = ns ++ n, n ∈ ns

Rule argument

indvar: # ns1 wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # ns1