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Proof step 7 from proof mods-zero-07 (previous step)

2 * i < 0, 2 * i + 1 < 0, 2 * i < i, 0 ≤ i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: modzero seq: ⊦ 0 < i ∧ abs(j0) < j → ¬ i * j + j0 < 0 subst: [j0, j, i] → [1, i, 2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i + (* j) < (* j0) ↔ i < j0 - j; (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; (ss)%zeroone: ⊦ 0 ≤ i ∧ i ≤ 1 → i = 0 ∨ i = 1; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs% ⊦ i < 1 ↔ i ≤ 0; (s) Used terms: 1, i, 2