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Proof step 1 from proof div-div-rec-01 (conclusion)

⊦ j < 0 ∧ 0 < i → (j - (2 ^ i - 1)) / 2 ^ i = ((j - (2 ^ (i - 1) - 1)) / 2 ^ (i - 1) - 1) / 2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: div-div-rec seq: ⊦ j < 0 ∧ 0 < i → ((j - (2 ^ i - 1)) / 2 ^ i - 1) / 2 = (j - (2 ^ (i + 1) - 1)) / 2 ^ (i + 1) subst: [i, j] → [i - 1, j] flags: rewrite, current

Additional information

Used simplifier rules: sub-sub-04: ⊦ i - (j - j0) = i + j0 - j; from specification int-abs%Sub-def: ⊦ 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%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%sub-eq-01: ⊦ i = j → i - j = 0; from specification int-abs%numsub: ⊦ (* i) + i0 - (* j) = (i - j) + i0; from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%one: ⊦ i / 1 = i; from specification int-div%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%minus-add: i < 0 ⊦ (* i) + j = j - ~ i; from specification int-abs Used terms: i - 1, j