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Proof step 65 from proof div-div-rec (previous step)

j1 < 0, 0 - j1 = 1, 0 < i, abs(j0) < 2 ^ i, j1 ≤ 0, j1 < i, i1 ≤ 0, i1 < i, j0 ≤ 0, j0 < i, 2 * i1 + j1 < 0, 2 ^ i * ((2 * i1 + j1) + 1) + j0 < 0, (2 * i1 + j1) + 1 < i, 0 ≤ i, 2 ^ i * (j1 + 2 * (i1 + 1)) + j0 ≤ 0, 2 ^ i * (j1 + 2 * (i1 + 1)) + j0 < i, 2 ^ i * 2 ≤ abs(2 ^ i * j1 + j0), 2 ^ i * j1 + j0 ≤ 0, 2 ^ i * j1 + j0 < i ⊦ i1 = (2 ^ i * (j1 + 2 * i1) + j0) / (2 ^ i * 2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
2 ^ i * 2 * i1 + j0 < 0, 2 ^ i * (2 * (i1 + 1) - 1) + j0 < i, 2 ^ i * (2 * (i1 + 1) - 1) + j0 ≤ 0, 2 * i1 < i, 0 ≤ i, 2 ^ i * 2 ≤ abs(j0 - 2 ^ i), j0 ≤ 2 ^ i, j0 < 2 ^ i + i, 0 < i, abs(j0) < 2 ^ i, i1 ≤ 0, i1 < i, j0 ≤ 0, j0 < i ⊦ i1 = (2 ^ i * (2 * i1 - 1) + j0) / (2 ^ i * 2)

Rule argument

Additional information

Used simplifier rules: 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-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%nummult-ls: ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 < (* j) ↔ i0 < (i + j - 1) / i); from specification int-div%add-zero: ⊦ i + 0 = i; from specification int-basic2%sub-le: ⊦ i - j ≤ i0 ↔ i ≤ j + i0; from specification int-abs%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%neg-15: ⊦ i + ~ j = i - j; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%minus-one-01: ⊦ i * ~1 = ~ i; from specification int-mult%minus-add: i < 0 ⊦ (* i) + j = j - ~ i; from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; 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%numadd-01: ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0; from specification int-abs%negeq: ⊦ ~ i = j ↔ i + j = 0; from specification int-abs%neg-06: ⊦ 0 - i = ~ i; from specification int-abs