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Proof step 7 from proof prepost-next2pot (previous step)

2exp-size(n0), 2exp-size(n1), n0 < minsize, minsize ≤ (minsize ≤ n0 * 2 ⊃ 0;minsize - n0 * 2) + n0 ⊦ minsize - n0 * 2 = 0

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [minsize, n0 * 2, n]

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ 2 * n ≤ n ↔ n = 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%m1 ≠ 0 ⊦ m < (* m1) * m + n0 ↔ (m1 - 1) * m + n0 ≠ 0; (s)% ⊦ m0 * 1 = m0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ ¬ 2exp-size(0); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n → m ≤ n; (s)% ⊦ n + 0 = n; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: minsize, n0 * 2, n