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Proof step 2 from proof sum-zero (previous step)

n∞ + n∞1 = ⌜0⌝ ⊦ n∞ = ⌜0⌝ ∧ n∞1 = ⌜0⌝

Heuristic structural induction applied rule structural induction

And closed the goal!

Rule argument

term: n∞1

Additional information

Used simplifier rules: add-all-inf: ⊦ n∞ + ∞ = ∞;%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2;%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1;%sum-zero-fin: ⊦ ⌜n⌝ + n∞ = ⌜0⌝ ↔ n∞ = ⌜0⌝ ∧ n = 0;%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2;%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1;%natinf freely generated by ∞, ⌜ ⌝;;%inj: ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; from specification nat-inf-basic%disj: ⊦ ⌜m⌝ ≠ ∞; from specification nat-inf-basic