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Proof step 1 from proof lemon2pot-01 (conclusion)

⊦ j ≤ 2 ^ n→i(m * n - 1) ∧ n ≤ n0 ∧ m ≠ 0 ∧ n ≠ 0 → j ≤ 2 ^ n→i(m * n0 - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: lemon2pot seq: ⊦ j ≤ 2 ^ i ∧ i ≤ i0 ∧ 0 ≤ i → j ≤ 2 ^ i0 subst: [j, i, i0] → [j, n→i(m * n - 1), n→i(m * n0 - 1)] flags: rewrite, current

Additional information

Used simplifier rules: ls-pos-2pot-01: 0 ≤ j ⊦ 2 ^ j < 2 ^ j0 ↔ j < j0;%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%le: ⊦ n→i(m) ≤ n→i(n) ↔ m ≤ n; from specification intnat%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%one-01: ⊦ m < 1 ↔ m = 0; from specification nat-basic1%zero-06: ⊦ m ≠ 0 → (m * n = 0 ↔ n = 0); from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%ls-03: n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0; from specification nat%nat2int: ⊦ 0 ≤ n→i(n); from specification intnat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%nat2int-04: ⊦ n→i(m) < n→i(n) ↔ m < n; from specification intnat%zero: ⊦ 0 * n = 0; from specification nat-mult%lez-01: ⊦ m ≤ 0 ↔ m = 0; from specification nat%ls-01: n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0; from specification nat%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%ls-02: ⊦ m0 ≠ 0 → (m0 * m < m0 * n ↔ m < n); from specification nat-mult%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: j, n→i(m * n - 1), n→i(m * n0 - 1)