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Proof step 49 from proof getsetShort-theorem (previous step)

0 < i, 0 ≤ i, 0 ≤ j0, i * 256 + j0 < 128 * 256 + 0, 127 < i, j0 < 256 ⊦ b2i(i2b(i)) = i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: numls-06 seq: ⊦ (* i2) * i + j < (* i1) * i + j0 ↔ (i2 - i1) * i + j < j0 subst: [j0, i1, j, i, i2] → [0, 128, j0, 256, i] flags: rewrite

Additional information

Used simplifier rules: forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%zero-ls: ⊦ 0 < i → (i * j < 0 ↔ j < 0); from specification int-mult%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%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%num-between: i + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j; from specification int-basic2 Used terms: 0, 128, j0, 256, i