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Proof step 9 from proof dec-nat-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: one-03: ⊦ 1 = m + 1 ↔ m = 0; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2%two-zero-01-01: ⊦ m / 2 = 0 ↔ ¬ ¬(m = 0 ∨ m = 1); from specification nat-div%zero: ⊦ 0 < m ↔ m ≠ 0; from specification nat-basic1%num-n2i-ls-02: 0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n; from specification intnat%neg-05: ⊦ ~ i < 0 ↔ 0 < i; from specification int-abs%n2n: ⊦ i→n(n→i(n)) = n; from specification intnat%abs-neg: ⊦ i→n(~ i) = i→n(i); from specification intnat