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Proof step 3 from proof zero-10 (previous step)

i / (n→i(n) + 1) < 0, i / (n→i(n) + 1) < i, 0 ≤ i ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-div name: zero-03 seq: ⊦ 0 < i ∧ 0 < j → 0 ≤ i / j subst: [i, j] → [i, n→i(n) + 1]

Additional information

Used simplifier rules: nat2int: ⊦ 0 ≤ n→i(n);%nat2int-07: ⊦ 0 ≠ n→i(m) + 1;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)% ⊦ ~1 < i ↔ 0 ≤ i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i < j → (j ≤ i ↔ false); (as)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%j ≠ 0 ⊦ 0 / j = 0; (s) Used terms: i, n→i(n) + 1