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Proof step 1 from proof two-padd (conclusion)

m < n ⊦ (m + n) / 2 < n

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: le-div-to-mult: m0 ≠ 0 ⊦ n ≤ m / m0 ↔ n * m0 ≤ m;%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%one: ⊦ m0 * 1 = m0; from specification nat-mult%numeral-26: m2 ≠ 0 ⊦ (* m2) * m ≤ m + n0 ↔ (m2 - 1) * m ≤ n0; from specification nat-mult%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat