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Proof step 26 from proof mod-ls-same-01 (previous step)

i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < abs(j) ∧ i0 ≤ 0 ∧ 0 ≤ i, j < i, j < 0, 0 < i, j + 1 < i ⊦ ~1 = j, j0 < i ↔ ¬ i + j < 0, i = 0, j = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
j0 + j < 0, 0 ≤ j0, j < i0 * j + j0, j + 1 < i0 * j + j0, j < 0, 0 < i0 * j + j0, i0 < i0 * j + j0, i0 ≤ 0, j + 1 < i0 * j ⊦ i0 < 0 ↔ ¬ (i0 * j + j0) + j < 0, ~1 = j, j = 1, i0 * j + j0 = 0

Rule argument

Additional information

Used simplifier rules: lst-03: ⊦ i + j < i0 ∧ ¬ j < j0 → i + j0 < i0; from specification int-basic2%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%ls-same-03: ⊦ i < 0 → (i < i * j ↔ j < 1); from specification int-mult%ls-01: ⊦ i + j < i + i0 ↔ j < i0; from specification int-basic2%succ-01: ⊦ i +1 = i + 1; from specification int-basic2%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%neg-07: ⊦ i < ~ j ↔ i + j < 0; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-gr-01: ⊦ i < 0 → (0 < i * j ↔ j < 0); from specification int-mult%ls-02: ⊦ i < i + j ↔ 0 < j; from specification int-basic2