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Proof step 12 from proof dec-nat-01 (previous step)

~ n→i((n + 1) / 2) < 0 ⊦ n % 2 = 0, 2 * i→n(~ n→i((n + 1) / 2)) - 1 = n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
⊦ n % 2 = 0, 2 * (n + 1) / 2 - 1 = n, n = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1; (ws)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)% ⊦ m / 2 = 0 ↔ m = 0 ∨ m = 1; (s)% ⊦ 0 < n ↔ n ≠ 0; (s)%0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n; (s)% ⊦ ~ i < 0 ↔ 0 < i; (s)% ⊦ i→n(n→i(n)) = n; (s)% ⊦ i→n(~ i) = i→n(i); (s)