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Proof step 6 from proof noeth-zero-ls (previous step)

0 < j + i * j, 0 ≤ i * j, 0 ≤ i + i1, 0 < j, i < 0, ∀ i0, j0. abs(i0) < i1 ∧ i0 ≠ 0 ∧ 0 < j0 → 0 < abs(i0) * j0 ⊦ i = 0

User applied rule all left

And closed the goal!

Rule argument

pos: left 6 terms: i + 1, j abort: F discard: F computed: F

Additional information

Used simplifier rules: minus-left: ⊦ ~ i * j = ~(i * j);%dist-lsplit: ⊦ (i + i0) * j = i * j + i0 * j;%one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%minus-one-02: ⊦ ~1 * i = ~ i;%abs-05: ⊦ i < 0 → abs(i + 1) = abs(i) - 1; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%subsub: ⊦ ~ i - j = ~(i + j); from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%neg-13: ⊦ ~ i < j ↔ 0 < j + i; from specification int-abs%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%numadd-01: ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0; from specification int-abs%neg: ⊦ 0 < ~ i ↔ i < 0; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%minus-add: i < 0 ⊦ (* i) + j = j - ~ i; from specification int-abs%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%negle-07: ⊦ i ≤ ~ j ↔ i + j ≤ 0; from specification int-abs%add-zero: ⊦ i + 0 = i; from specification int-basic2%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: i + 1, j