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Proof step 2 from proof nonumsimp-twonle (previous step)

2 * n ≤ m + m0, m < n, m0 ≤ n ⊦ n = 0

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 3:
m ≤ m0, n < n0 ⊦ m + n < m0 + n0

Rule argument

spec: nat inst: name: pls seq: m ≤ m0, n < n0 ⊦ m + n < m0 + n0 subst: [m, m0, n, n0] → [2 * n, m + m0, m, n] flags:

Additional information

Used simplifier rules: numeral-27: m2 ≠ 0 ⊦ (* m2) * m < m + n0 ↔ (m2 - 1) * m < n0;%one: ⊦ m0 * 1 = m0;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%l: ⊦ m + n < m + n0 ↔ n < n0; from specification nat-basic2%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: 2 * n, m + m0, m, n