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Proof step 3 from proof is-encoded-unique (previous step)

is-encoded(nx0, buf), is-encoded(nx1, buf) ⊦ nx0 = nx1

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
is-encoded(m + nx, buf), is-encoded(nx0, buf), ∀ nx0, buf. is-encoded(nx0, buf) ∧ is-encoded(nx, buf) → nx0 = nx ⊦ nx0 = m + nx

Rule argument

term: nx1

Additional information

Used simplifier rules: is-encoded-base: ⊦ is-encoded([], buf) ↔ buf = mkbuf(0);%is-encoded-empty: ⊦ is-encoded(nx, mkbuf(0)) ↔ nx = [];%nat-list freely generated by [], +;;